If (\sin x+\cos x=\frac{7}{5}), what is the value of (\tan x+\cot x)?

Question

Answer and explanation

Correct answer: (\frac{25}{12})

Squaring gives (1+2\sin x\cos x=\frac{49}{25}), so (\sin x\cos x=\frac{12}{25}). Now (\tan x+\cot x=\frac{1}{\sin x\cos x}=\frac{25}{12}).

What is the correct answer to this question?

(\frac{25}{12})

Why is this the correct answer?

Squaring gives (1+2\sin x\cos x=\frac{49}{25}), so (\sin x\cos x=\frac{12}{25}). Now (\tan x+\cot x=\frac{1}{\sin x\cos x}=\frac{25}{12}).

Which subject and chapter does this question cover?

This is a Class 12 Mathematics question. Chapter: Trigonometric Functions. Topic: Trigonometric functions and their properties.