i need to show that the given equation is an identity. using composite argument properties.

Question

(cosAcosB-sinAsinb)^2 + (sinAcosB+cosAsinB)^2 = 1

Composite argument properties:

cos(A + B) = cosAcosB - sinAsinB
sin(A + B) = sinAcosB + cosAsinB

Substituting:

[cos(A + B)]^2 + [sin(A + B)]^2 = 1

Can you take it from here?

Answer 1

Sin^2(x) + cos^2(x) = 1
Answer is this. So easy way.