Question

(sin(theta/2)+cos(theta/2))^2 = 1+sin(x)

Answer 1

establish identity

Answer 2

expand the equation and use pythagoraus theorem

Answer 3

ok... so expand the left hand side

\[\sin^2(\frac{\theta}{2}) + 2\sin(\frac{\theta}{2})\cos(\frac{\theta}{2}) + \cos^2(\frac{\theta}{2})\]

now sin^2 + cos^2 = 1

so you problem is now

\[1 + 2\sin(\frac{\theta}{2})\cos(\frac{\theta}{2})\]

and you should know

sin(2a) = 2sin(a)cos(a)

apply this trig identity to the simplification above.

hope it helps

Answer 4

think about a = @/2