Question

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

Answer 1

Answer:

sin² (x) + cos²(x) = 1  

Step-by-step explanation:

(sin a cosB + cos a sin B)² + (cos a cos B - sin a sin B)² = 1

sin(a + B) = sin a cos B + cos a sin B

cos(a + B) = cos a cos B - sin a sin B

(sin(a + B))² + (cos(a + B))² = 1

sin² (x) + cos²(x) = 1       Identity

 

sin² (a + B) + cos²(a + B) = 1    the same angle

1 = 1     is True