Q10 of 123 Page 9

Prove that:
For all values of x.

We know

sin (A+B)sin (A–B)=sin²A–sin²B

So the above LHS becomes,

But 3sin x–4 sin³x=sin 3x

But |sin θ|≤ 1 for all values of x

Hence

Therefore For all values of x

Prove that:

sin 5x = 5 cos⁴x sin x – 10 cos²x sin³ x + sin⁵ x

Prove that:

for all values of x

Prove that:

Prove that:For all values of x.