First slide

Trigonometric Identities

Question

The value of $\frac{2 \cos^{3} (\frac{π}{2} + x) \cot (3 π + x) \sec (x - 3 π) cosec (3 \frac{π}{2} - x)}{\cot {xtan}^{2} (x - π) \sin (x - 2 π)}$ is equal to

Moderate

A

0
B

-1
C

-2
D

1

Solution

we have,
$\begin{matrix} \frac{2 \cos^{3} (\frac{π}{2} + x) \cot (3 π + x) \sec (x - 3 π) cosec (3 \frac{π}{2} - x)}{\cot {xtan}^{2} (x - π) \sin (x - 2 π)} \\ = \frac{2 (- \sin^{3} x) (\cot x) (- \sec x) (- \sec x)}{\cot {xtan}^{2} xsin x} \\ = - 2 \end{matrix}$

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