Can someone explain how: (sin(a)cos(b))^2 + (sin(a)sin(b))^2 + (cos(a))^2 is equal to 1?

Question

Can someone explain how: (sin(a)cos(b))^2 + (sin(a)sin(b))^2 + (cos(a))^2 is equal to 1?

Answer 1

(sin a cos b)^2 + (sin a sin b)^2+ (cos a)^2 = 1

(sin^2 a cos^2 b) + (sin^2 a sin^2 b) + (cos^2 a) = 1

[sin^2 a] (cos^2 b + sin^2 b) +(cos^2 a) = 1

Remember that “sin^2 a + cos^2 a = 1” and “sin^2 b + cos^2 b = 1” (the angles have to be the same for that property to work!)

[sin^2 a] (1) + (cos^2 a) = 1

sin^2 a + cos^2 a = 1

Answer 2

(sin(a)cos(b))^2 + (sin(a)sin(b))^2 + (cos(a))^2

= sin^2(a)cos^2(b) + sin^2(a)sin^2(b) + cos^2(a)

= sin^2(a) [cos^2(b) + sin^2(b)] + cos^2(a)

= sin^2(a) [1] + cos^2(a)

=1