Assertion: ( cos (π+x) ⋅ cos (-x)/ sin (π-x) ⋅ cos ((π)2+x))= cot 2 x Reason: cos (π+θ)=- cos θ and cos (-θ)= cos θ Also, sin (π-θ)= sin θ and sin (-θ)=- sin θ

Question

Assertion: ( cos (π+x) ⋅ cos (-x)/ sin (π-x) ⋅ cos ((π)2+x))= cot 2 x Reason: cos (π+θ)=- cos θ and cos (-θ)= cos θ Also, sin (π-θ)= sin θ and sin (-θ)=- sin θ (A) Assertion is correct, reason is correct; reason is a correct explanation for assertion. (B) Assertion is correct, reason is correct; reason is not a correct explanation for assertion (C) Assertion is correct, reason is incorrect (D) Assertion is incorrect, reason is correct.

Tardigrade Admin · Accepted Answer

( cos (π+x) cos (-x)/ sin (π-x) cos ((π)2+x))=((- cos x)( cos x)/( sin x)(- sin x)) =( cos 2 x/ sin 2 x)= cot 2 x

Q. Assertion $: \frac{c o s ( π + x ) \cdot c o s ( - x )}{s i n ( π - x ) \cdot c o s ( \frac{π}{2} + x )} = cot^{2} x$
Reason $: cos (π + θ) = - cos θ$ and $cos (- θ) = cos θ$
Also, $sin (π - θ) = sin θ$ and $sin (- θ) = - sin θ$

Assertion is correct, reason is correct; reason is a correct explanation for assertion.

Assertion is correct, reason is correct; reason is not a correct explanation for assertion

Assertion is correct, reason is incorrect

Assertion is incorrect, reason is correct.

$\frac{c o s ( π + x ) c o s ( - x )}{s i n ( π - x ) c o s ( \frac{π}{2} + x )} = \frac{( - c o s x ) ( c o s x )}{( s i n x ) ( - s i n x )}$
$= \frac{c o s ^{2} x}{s i n ^{2} x} = cot^{2} x$

Q. Assertion :sin(π−x)⋅cos(2π​+x)cos(π+x)⋅cos(−x)​=cot2x Reason :cos(π+θ)=−cosθ and cos(−θ)=cosθ Also, sin(π−θ)=sinθ and sin(−θ)=−sinθ