Question

prove that trigonometric : cos (π/2-x)=sin x​

Answer 1

Answer:

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)