Question

The value of $2(\sin^{6}\theta + \cos^{6}\theta) - 3(\sin^{4}\theta + \cos^{4}\theta) + 1$ is

• A. 2
• B. 0
• C. 4
• D. 6

Answer 1

Answer: (B)

0

Answer 2

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

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

and $\sin^{4}\theta + \cos^{4}\theta + 2\sin^{2}\theta\cos^{2}\theta = 1$

Both gives, $2(\sin^{6}\theta + \cos^{6}\theta) - 3(\sin^{4}\theta + \cos^{4}\theta) + 1 = 0$.