Question

Sin 4 theta+sin 4 3theta + sin 4 5theta + sin 4 7theta , theta =pi/ 16​

Answer 1

Answer:

3/2

Step-by-step explanation:

since sin^4 theta and sin^4 7 theta are complementary,

and sin^4 3 theta and sin^4 5 theta are complementary

⇒sin^4 theta+ cos^4 theta + sin^43 theta+cos^4 3 theta

= (sin^2 theta+cos^2 theta)^2- 2 sin^2 theta cos^2 thta+(sin^2 3 theta + cos^2 3 theta_ - 2 sin^2 3 theta cos^2 3 theta

= 2-2(sin^2 theta cos^2 theta + sin^2 3 theta cos^2 3 theta)

= 2-2/4(sin^2 2 theta+sin^26theta)

⇒2-1/2(1)

⇒3/2