If $cosx$ $+ \cos^{2} x = 1$ then $\sin^{12} x + 3 \sin^{10} x +$ $3 \sin^{8} x + \sin^{6} x + \sin^{4} x + 2 \sin^{2} x - 2$ is equal to ?

see full answer

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

0

sinx

1 - cosx

1

answer is C.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

Given that,

\Rightarrow cosx = 1 - \cos^{2} x

\Rightarrow cosx = \sin^{2} x

We need to find the value of

\sin^{12} x + 3 \sin^{10} x +

3 \sin^{8} x + \sin^{6} x + \sin^{4} x + 2 \sin^{2} x - 2

.
Now, in the given equation let us substitute

\sin^{2} x = cosx

= cos 6 x + 3 cos 5 x + 3 cos 4 x + cos 3 x + 2 cos 2 x + cos x − 2 = cos 3 x (cos x + 1) 3 + 2 cos 2 x + cos x − 2 = (cos 2 x + cos x) 3 + cos x − 2 (1 − cos 2 x) = (1) 3 + c o s x − 2 c o s x = 1 − c o s x

So, the value of the expression

\sin^{12} x + 3 \sin^{10} x +

3 \sin^{8} x + \sin^{6} x + \sin^{4} x + 2 \sin^{2} x - 2

1 - cosx

.
Hence, the correct option is (3).

Watch 3-min video & get full concept clarity