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Mathematics Trigonometric functions and their properties MCQ Questions for Class 11

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Trigonometric functions and their properties Practice Questions

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Question 161/350 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 70

फलन \(5-2\cos x\) का न्यूनतम मान क्या है?

What is the minimum value of the function \(5-2\cos x\)?

Explanation opens after your attempt
Correct Answer

B. 3

Explanation

Simple Explanation

चूँकि \(\cos x\) का मान \(-1\) से \(1\) के बीच होता है, इसलिए \(5-2\cos x\) न्यूनतम तब होगा जब \(\cos x=1\) हो। अतः न्यूनतम मान \(5-2(1)=3\) है। \(7\) अधिकतम मान है, जो \(\cos x=-1\) पर मिलता है। परीक्षा टिप: ऋणात्मक गुणांक वाले त्रिकोणमितीय पद में फलन का न्यूनतम ज्ञात करने के लिए उस त्रिकोणमितीय फलन का अधिकतम मान लें। / Since \(\cos x\) lies between \(-1\) and \(1\), \(5-2\cos x\) is smallest when \(\cos x=1\). Thus, its minimum value is \(5-2(1)=3\). The value \(7\) is the maximum, obtained when \(\cos x=-1\). Exam tip: For a trigonometric term with a negative coefficient, use the maximum value of that trigonometric function to find the minimum of the expression.

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Question 162/350 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 70

यदि \(\sin x=\frac{5}{13}\) और (x) प्रथम चतुर्थांश में है, तो \(\tan x\) का मान क्या है?

If \(\sin x=\frac{5}{13}\) and (x) is in the first quadrant, what is the value of \(\tan x\)?

Explanation opens after your attempt
Correct Answer

C. \(\frac{5}{12}\)

Explanation

Simple Explanation

\(\cos x=\frac{12}{13}\) और \(\tan x=\frac{\sin x}{\cos x}\) होगा। इसलिए \(\tan x=\frac{5}{12}\)। / \(\cos x=\frac{12}{13}\) and \(\tan x=\frac{\sin x}{\cos x}\). Hence \(\tan x=\frac{5}{12}\).

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Question 163/350 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 70

यदि \(\cos x=\frac{8}{17}\) और (x) प्रथम चतुर्थांश में है, तो \(\cot x\) का मान क्या है?

If \(\cos x=\frac{8}{17}\) and (x) is in the first quadrant, what is the value of \(\cot x\)?

Explanation opens after your attempt
Correct Answer

A. \(\frac{8}{15}\)

Explanation

Simple Explanation

\(\sin x=\frac{15}{17}\) मिलता है और \(\cot x=\frac{\cos x}{\sin x}\) होता है। इसलिए \(\cot x=\frac{8}{15}\)। / \(\sin x=\frac{15}{17}\) and \(\cot x=\frac{\cos x}{\sin x}\). Therefore, \(\cot x=\frac{8}{15}\).

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Question 164/350 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 70

यदि \(\tan x=\frac{3}{4}\) और (x) प्रथम चतुर्थांश में है, तो \(\sin x\) का मान क्या है?

If \(\tan x=\frac{3}{4}\) and (x) is in the first quadrant, what is the value of \(\sin x\)?

Explanation opens after your attempt
Correct Answer

B. \(\frac{3}{5}\)

Explanation

Simple Explanation

\(\tan x=\frac{3}{4}\) से समकोण त्रिभुज में कर्ण (5) होगा। इसलिए \(\sin x=\frac{3}{5}\)। / From \(\tan x=\frac{3}{4}\), the hypotenuse in a right triangle is (5). Hence \(\sin x=\frac{3}{5}\).

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Question 165/350 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 70

यदि \(\cot x=\frac{5}{12}\) और (x) प्रथम चतुर्थांश में है, तो \(\cos x\) का मान क्या है?

If \(\cot x=\frac{5}{12}\) and (x) is in the first quadrant, what is the value of \(\cos x\)?

Explanation opens after your attempt
Correct Answer

C. \(\frac{5}{13}\)

Explanation

Simple Explanation

\(\cot x=\frac{5}{12}\) में आसन्न (5) और सामने (12) मानें। कर्ण (13) होगा, इसलिए \(\cos x=\frac{5}{13}\)। / For \(\cot x=\frac{5}{12}\), take adjacent as (5) and opposite as (12). The hypotenuse is (13), so \(\cos x=\frac{5}{13}\).

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Question 166/350 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 70

\(\sin(\pi+x)+\sin(\pi-x)\) का सरल मान क्या है?

What is the simplified value of \(\sin(\pi+x)+\sin(\pi-x)\)?

Explanation opens after your attempt
Correct Answer

B. \(0\)

Explanation

Simple Explanation

पूरक कोण सूत्रों के अनुसार \(\sin(\pi+x)=-\sin x\) तथा \(\sin(\pi-x)=\sin x\) होता है। अतः \(\sin(\pi+x)+\sin(\pi-x)=-\sin x+\sin x=0\)। \(2\sin x\) तब मिलता है जब दोनों पद \(\sin x\) के समान चिह्न वाले हों, जो यहाँ नहीं है। परीक्षा टिप: \(\pi\pm x\) वाले कोणों में चिन्ह निर्धारित करने के लिए कोण का चतुर्थांश अवश्य देखें। / Using allied-angle identities, \(\sin(\pi+x)=-\sin x\) and \(\sin(\pi-x)=\sin x\). Therefore, \(\sin(\pi+x)+\sin(\pi-x)=-\sin x+\sin x=0\). The result \(2\sin x\) would occur only if both terms had the same sign, which they do not here. Exam tip: for angles of the form \(\pi\pm x\), determine the sign by identifying the quadrant.

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Question 167/350 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 70

\(\cos(\pi+x)+\cos(\pi-x)\) का सरल मान क्या है?

What is the simplified value of \(\cos(\pi+x)+\cos(\pi-x)\)?

Explanation opens after your attempt
Correct Answer

A. \(-2\cos x\)

Explanation

Simple Explanation

पूरक कोण के सूत्रों से \(\cos(\pi+x)=-\cos x\) तथा \(\cos(\pi-x)=-\cos x\) होता है। अतः \(\cos(\pi+x)+\cos(\pi-x)=-\cos x-\cos x=-2\cos x\)। \(0\) केवल विशेष मानों, जैसे \(\cos x=0\), के लिए मिल सकता है; यह सामान्य सरल रूप नहीं है। परीक्षा टिप: \(\pi\pm x\) वाले कोणों में पहले त्रिकोणमितीय फलन का चिह्न जाँचें। / Using allied-angle identities, \(\cos(\pi+x)=-\cos x\) and \(\cos(\pi-x)=-\cos x\). Hence, \(\cos(\pi+x)+\cos(\pi-x)=-\cos x-\cos x=-2\cos x\). The value \(0\) may occur only for particular values such as when \(\cos x=0\); it is not the general simplified form. Exam tip: For angles of the form \(\pi\pm x\), first check the sign of the trigonometric function.

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Question 168/350 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 70

\(\tan(\pi+x)-\tan(\pi-x)\) का सरल मान क्या है?

What is the simplified value of \(\tan(\pi+x)-\tan(\pi-x)\)?

Explanation opens after your attempt
Correct Answer

C. \(2\tan x\)

Explanation

Simple Explanation

\(\tan\) का आवर्त \(\pi\) है, इसलिए \(\tan(\pi+x)=\tan x\)। साथ ही, \(\tan(\pi-x)=\tan(-x)=-\tan x\)। अतः \(\tan(\pi+x)-\tan(\pi-x)=\tan x-(-\tan x)=2\tan x\)। \(-2\tan x\) तब मिलता यदि पदों का क्रम उलटा होता। परीक्षा टिप: \(\tan(\pi-x)\) में ऋण चिह्न अवश्य ध्यान रखें। / The period of \(\tan\) is \(\pi\), so \(\tan(\pi+x)=\tan x\). Also, \(\tan(\pi-x)=\tan(-x)=-\tan x\). Hence, \(\tan(\pi+x)-\tan(\pi-x)=\tan x-(-\tan x)=2\tan x\). The value \(-2\tan x\) would result if the order of the two terms were reversed. Exam tip: carefully retain the negative sign in \(\tan(\pi-x)\).

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Question 169/350 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 70

(\sin\(\frac{\pi}{2}+x\)) किसके बराबर है?

What is (\sin\(\frac{\pi}{2}+x\)) equal to?

Explanation opens after your attempt
Correct Answer

D. \(\cos x\)

Explanation

Simple Explanation

\(\frac{\pi}{2}+x\) वाले रूप में \(\sin\) बदलकर \(\cos\) होता है और चिन्ह धनात्मक रहता है। इसलिए उत्तर \(\cos x\) है। / In the form \(\frac{\pi}{2}+x\), \(\sin\) changes to \(\cos\) and the sign remains positive. Hence the answer is \(\cos x\).

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Question 170/350 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 70

(\cos\(\frac{\pi}{2}+x\)) किसके बराबर है?

What is (\cos\(\frac{\pi}{2}+x\)) equal to?

Explanation opens after your attempt
Correct Answer

B. \(-\sin x\)

Explanation

Simple Explanation

\(\frac{\pi}{2}+x\) वाले रूप में \(\cos\) बदलकर \(\sin\) होता है और चिन्ह ऋणात्मक होता है। इसलिए \(-\sin x\) मिलता है। / In the form \(\frac{\pi}{2}+x\), \(\cos\) changes to \(\sin\) with a negative sign. Hence it becomes \(-\sin x\).

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