Question

if 8 sin theta×cos theta×cos 2 theta ×cos 4theta=sin x,then x=

Answer 1

Answer:

Step-by-step explanation:

we known: sin 2@=2 sin@ cos@

8 sin@ cos@ cos2@ cos4@=sin x

2 2 (2 sin@ cos@) cos2@ cos4@=sin x

2 (2 (sin2@) cos2@) cos4@=sin x

2 sin4@ cos4@=sin x

sin 8@=sin x

(@=theta)

therefore, x = 8 theta

Answer 2

Given: Here we have given 8 sin theta×cos theta×cos 2 theta ×cos 4theta=sin x

To find: we have to find the value of x

Solution:

Here we know that $sin 2\theta=2 sin\theta cos\theta$

$8 sin\theta cos\theta cos2\theta cos4\theta=sin x \\2 \times 2 \times (2 sin\theta cos\theta) cos2\theta cos4\theta=sin x\\2 \times (2 (sin2\theta) cos2\theta) cos4\theta=sin x\\2 sin4\theta cos4\theta=sin x\\sin 8\theta=sin x$

Here we will multiply both side by $sin^-1$

therefore, $x = 8 \theta$

Final answer:

Hence the answer is $x = 8 \theta$