Prove that the equation is an identity...?

Question

My math final is tomorrow and I know the study guide front to back except for this problem it says the following: Prove that the given equation is an identity.

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

Answer 1

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

cos(pi/2) = 0 ; sin(pi/2) = 1

SO..

sin (x-(pi/2)) = (sin x )*0 - (cos x )*1 = - cos x

Answer 2

You can use the following identity,
sin(a-b)=sin(a)cos(b)-cos(a)sin(b)

and remember sin(pi/2)=1 and cos(pi/2)=0.

Good luck.

Answer 3

LHS = sin (x - π/2)
= sin x.cos π/2 - cos x.sin π/2
= 0 - cos x.1
= - cos x
= RHS

Answer 4

this is correct

sin (x - 90 ) = sin x cos 90 - sin 90 cos x
. . . . . .= 0 - cos x
. . . . . .= - cos x

Answer 5

LHS sin ² ? / cos ² ? - sin ² ? sin ² ? - sin ² ? cos ² ? ------------------------------- cos ² ? sin ² ? ( one million - cos ² ? ) -------------------------- cos ² ? tan ² ? ( one million - cos ² ? ) tan ² ? sin ² ? RHS tan ² ? sin ² ? LHS = RHS