Question

Prove that:
3. (sin a cos B+ cos a sin B)2 + (cos a cos B - sin a sin B)2 = 1.
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Answer 1

Step-by-step explanation:

The following two equation help us.

you needn't memorize these as you will encounter these formulas so many times that I am sure after few practice you will be able to identify them.

1. sin(A+B) = sinAcosB + cosAsinB

2. cos(A+B) = cosAcosB - sinAsinB

3. sin^2(A+B) + cos^2(A+B) = 1

now, according to your question

(sinAcosB + cosAsinB)^2 + (cosAcosB - sinAsinB)^2

= {sin(A+B)}^2 + {cos(A+B)}^2

= sin^2(A+B) + cos^2(A+B)

= 1 = RHS

Hence proved! :)

Answer 2

I hope answer is helpful to us us