Question

If $sin6\theta =32co{s}^5\theta sin\theta -32co{s}^3\theta sin\theta +3x,$ then x=

• A. $cos\theta$
• B. $cos2\theta$
• C. $sin\theta$
• D. $sin2\theta$

Answer 1

The correct option is D $sin2\theta$

$sin6\theta =2sin3\theta cos3\theta$
$=2[3sin\theta -4si{n}^3\theta ][4co{s}^3\theta -3co{s}^3\theta ]$
$=24sin\theta cos\theta (si{n}^2\theta +co{s}^2\theta )-18sin\theta cos\theta -32si{n}^2\theta co{s}^2\theta$
$=32co{s}^5\theta sin\theta -32co{s}^3\theta sin\theta +3sin2\theta$
On comparing, $x=sin2\theta .$