Question

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

Answer 1

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)