Question

Prove that : cos ( pie / 2 + x ) sec (-x) tan (pie -x) / sec ( 2 pie - x ) sin (pie + x) cot (pie /2 - x ) = -1​

Answer 1

Answer:

Step-by-step explanation:

we will first simplify those pie figures

cos(pi/2 +x)= -sin(x)

sec(-x)=1/cos(-x) = 1/cos(x)

tan(pi - x) = -tan(x)

sec(2pi - x) = 1/cos(2 pi -x) = 1/cos(x)

sin( pi + x)= -sin( x)

cot( pi/2 - x)= tan(x)

now feeding these values in eqn

cos ( pie / 2 + x ) sec (-x) tan (pie -x) / sec ( 2 pie - x ) sin (pie + x) cot (pie /2 - x )

=[-sin x * 1/cos x *- tan x] / [1/cos x * -sin x * tan x]

=[(sin x/cos x )* tan x] / [(-sin x /cos x) * tan x]

=[(sin x/cos x )* tan x] / -1 *[(sin x/cos x )* tan x]

= -1

Hope it helps :-)