Question

Use the trigonometric subtraction formula for sine to verify this identity:

cos((π / 2) – x) = sin x

Answer 1

cos(pi/2 - x)

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

= (0)cos(x) + (1)sin(x)

= sin(x)

Verification

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

cos(0) = sin(pi/2)

1 = 1

Answer 2

Explanation:

The simplest way to prove

cos(π/2 - x) = sin x

is to put A = π/2 , B = x in the trigonometric formula

cos(A-B) = cos A . cos B + sin A . sin B……………………………….(1)

and obtain

cos(π/2 - x) = cos π/2 . cos x + sin π/2 . sin x……………………….(2)

Substituting cos π/2 = 0 and sin π/2 = 1 in (2),

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

∴cos (π/2 - x) = sin x (Proved)