Question

Prove that sin 33+cos 63=cos 3

Answer 1

sin 33+cos 63=cos 3

Step-by-step explanation:

sin 33+cos 63=cos 3

LHS = Sin33 + Cos 63

Sin33 = Sin(30 + 3)

Cos63 = Cos(60 + 3)

Sin (A + B) = SinaCosB + CosASinB

Cos(A + B) = CosA CosB - SinASinB

= Sin30Cos3 + Cos30Sin3  + Cos60Cos3 - Sin60Sin3

= Sin30Cos3 + Cos60Cos3 + Cos30Sin3 - Sin60Sin3

As we know that Cosα = Sin(90 - α)  

=> Cos60 = Sin30  & Cos30 = SIn60

= Sin30Cos3 + Sin30Cos3 + Sin60Sin3 - Sin60Sin3

= 2 Sin30Cos3

Sin30 = 1/2

=> 2Sin30 = 1

= Cos3

= RHS

QED

Proved

sin 33+cos 63=cos 3