Question

Prove that
cos^2(pi/2_thita/4)_sin^2(pi/4_thita/4)=sin thita/2

please help me..

Answer 1

See below.

Step-by-step explanation:

Using the identity sin^2x - sin^2x = cos 2x

cos^2( π/4 - Ф/4) - sin^2(π/4 - Ф/4) = cos 2(π/4 - Ф/4)

= cos(π/2 - Ф/2)

Now cos(π/2 - Ф/2) = cosπ/2 cos Ф/2 + sin π/2 sin Ф/2

But cos π/2 = 0 and sin π/2 = 1 so

cos(π/2 - Ф/2) = 0 * cos Ф/2 + 1 * sin Ф/2

= sin Ф/2.