If A is an acute angle, the simplified form of

\(\rm \frac{{\cos (\pi - A).\cot \left( {\frac{\pi }{2} + A} \right)\cos ( - A)}}{{\tan (\pi + A)\tan \left( {\frac{{3\pi }}{2} + A} \right)\sin (2\pi - A)}}\)is :

Question

Question

This question was previously asked in

SSC CGL 2022 Tier-I Official Paper (Held On : 13 Dec 2022 Shift 4)

Answer 1

Concept used:
F4 Vinanti SSC 02.05.23 D1

Formula used:

Calculation:

\(\rm \frac{{\cos (π - A).\cot \left( {\frac{π }{2} + A} \right)\cos ( - A)}}{{\tan (π + A)\tan \left( {\frac{{3π }}{2} + A} \right)\sin (2π - A)}}\)

By using the above formula
\(\rm \frac{{\ (-cos A)\ . \ ( {-tan A} )\ \ .\ cos A}}{{\tan A\ .\ (-cot A ).\ (-sin A)}}\)

⇒ \(\frac{cos A\ .\ cos A}{cot A\ . \ sin A}\)

But, cos θ / sin θ = cot θ

⇒ cot A. cos A/ cot A

⇒ cos A

∴ The correct answer is cos A.

Download Solution PDF