Question

Prove that sin 6 theta + cos 6 theta + 3 sin square theta into cos square theta = 21

Answer 1

See the attached pic.

Answer 2

Answer:

Step-by-step explanation:

The given equation is:

$sin^6{\theta}+cos^6{\theta}+3sin^2{\theta}cos^2{\theta}$

We know that $(sin^2{\theta}+cos^2{\theta})=1$

Cubing on both the sides of the above equation, we get

$(sin^2{\theta}+cos^2{\theta})^3=1$

$(sin^2{\theta}^3+(cos^2{\theta})^3+3sin^2{\theta}cos^2{\theta}(sin^2{\theta}+cos^2{\theta})=1$

$sin^6{\theta}+cos^6{\theta}+3sin^2{\theta}cos^2{\theta}=1$

Hence proved.