Question

[cos(270-x) + Cos(360-x)]² + [sin (90-x) + sin(180-x)]²

Answer 1

Answer:sin(180+x)=-sinx

cos(90+x)=-sinx

tan(270-x)=cotx

cot(360-x)=-cotx

sin(360-x)=-sinx

cos(360+x)=cosx

cosec(-x)=-cosecx

sin(270+x)=-cosx

therefore,

sin(180+x)cos(90+x)tan(270-x)cot(360-x)÷sin(360-x)cos(360+x)cosec(-x)sin(270+x)

=(-sinx)(-sinx)(cotx)(-cotx)÷(-sinx)(cosx)(-cosecx)(-cosx)

=(-sin x)(-sinx)(cosx/sinx)(-cosx/sinx)÷(-sinx)(cosx)(-1/sinx)(-cosx)

=1

Answer 2

Answer:

cos (90+x) sec (270+x) sin (180+x) /cosec(-x) cos (270-x) tan (180+x).

=> {(-sin x)(cosec x)(-sin x)} / {(-cosec x)(-sin x)(tan x)}.

=> {sin²x cosec x} / {cosec x sin x (sin x / cos x)}.

=> {sin²x cosec x} / {(sin²x cosec x)/cos x}.

=> {(sin²x cosec x)(cos x)} / {(sin²x cosec x)}.

=> (sin²x cosec x)(cos x) / (sin²x cosec x).

=> cos x.

=> cos x.=> 1.

$thanks$