Cos (pi/2 - x) = sin x is this true or false?

The above statement is true meaning cos (π/₂-x) = sin (x)

Step-by-step explanation:

We know that sine and cosine function are mutual cofunctions.

Hence this would mean that these two functions are complimentary of each other meaning cos (π/₂-x) = sin (x)

This can be verified mathematically by assuming "x" as 30°

Hence Cos (π/₂-30°) = cos 60° = 0.5 (from trigonometric table values)

Similarly Sin 30° = 0.5 (from trigonometric table values)

This can be proved through using the formula

Cos (A-B) = Cos A. Cos B + Sin A. Sin B

Here A=90° and b=x°

Putting the values we get (it is to be remembered that cos 90°=0 and sin 90°=1)

Cos 90°. cos x + sin 90. sin x

0+sinx = sinx

Hence it is proved that cos (π/₂-x) = sin (x)