The value of cos ( (3π /2)+x ) cos (2π +x) cot ( (3π /2)-x )+ cot (2π +x) is

Question

The value of cos ( (3π /2)+x ) cos (2π +x) cot ( (3π /2)-x )+ cot (2π +x) is (A)  0  (B)  1  (C)  cos text x  (D)  sin text x

Tardigrade Admin · Accepted Answer

cos ( (3π /2)+x ) cos (2π +x) cot ( (3π /2)-x ) + cot (2π +x) = sin x. cos x ( tan x+ cot x = sin x. cos x( ( sin 2x+ cos 2x/ sin x. cos x) ) =1 (∵ sin 2θ + cos 2θ =1)

Q. The value of $cos (\frac{3 π}{2} + x) cos (2 π + x) {cot (\frac{3 π}{2} - x) + cot (2 π + x)}$ is

$0$

$1$

$cos x$

$s in x$

$cos (\frac{3 π}{2} + x) cos (2 π + x)$
${cot (\frac{3 π}{2} - x) + cot (2 π + x)}$ $= sin x . cos x (tan x + cot x}$
$= sin x . cos x (\frac{s i n ^{2} x + c o s ^{2} x}{s i n x . c o s x})$
$= 1$
$(∵ sin^{2} θ + cos^{2} θ = 1)$

Q. The value of cos(23π​+x)cos(2π+x){cot(23π​−x)+cot(2π+x)} is

0

1

cosx

sinx

cos(23π​+x)cos(2π+x) {cot(23π​−x)+cot(2π+x)} =sinx.cosx(tanx+cotx} =sinx.cosx(sinx.cosxsin2x+cos2x​) =1 (∵sin2θ+cos2θ=1)

Q. The value of $cos (\frac{3 π}{2} + x) cos (2 π + x) {cot (\frac{3 π}{2} - x) + cot (2 π + x)}$ is

$0$

$1$

$cos x$

$s in x$

$cos (\frac{3 π}{2} + x) cos (2 π + x)$
${cot (\frac{3 π}{2} - x) + cot (2 π + x)}$ $= sin x . cos x (tan x + cot x}$
$= sin x . cos x (\frac{s i n ^{2} x + c o s ^{2} x}{s i n x . c o s x})$
$= 1$
$(∵ sin^{2} θ + cos^{2} θ = 1)$