Trigonometry & Inverse Trigonometry
Trigonometry
star_batch_jee_advanced_2025
Grade 11
Question:
The value of $\frac{\sin x-\cos x}{\sin^3 x}$ is equal to:
$\cosec^2 x(1-\cot x)$
$1-\cot x+\cot^2 x-\cot^3 x$
$\cosec^2 x-\cot x-\cot^3 x$
$\frac{1-\cot x}{\sin^2 x}$
Step-by-Step Solution
Key Concept: Proving trigonometric identities often requires strategic factorization using Pythagorean relationships like $\csc^2 x = 1 + \cot^2 x$.
Starting with $\frac{(1-\cot x)}{\sin^2 x} = (1-\cot x)\cdot\csc^2 x = (1-\cot x)(1+\cot^2 x) = (1-\cot x)(1+\cot x)^2 + (1-\cot x)\cot^2 x$, which simplifies to the right-hand side after algebraic manipulation using $\csc^2 x = 1 + \cot^2 x$.
Correct Answer: 1,2,3,4