इन समीकरण को हल कीजिये `sin 7 theta=cos theta`

The number of values of theta in (0, pi] , such that (cos theta + i sin theta) (cos 3 theta + i sin 3 theta) (cos 5 theta + i sin 5 theta) (cos 7 theta + i sin 7 theta) (cos 9 theta + i sin 9 theta) = -1 is

cos theta-cos7 theta=sin4 theta

Prove the following : sin theta+ sin 3 theta+ sin 5 theta+sin 7 theta=4 cos theta cos2 theta sin4 theta .

Prove the following identities : (sin theta +sin 3 theta + sin 5 theta + sin 7theta)/(cos theta + cos 3 theta + cos 5 theta + cos 7 theta)=tan 4 theta

Prove that (sin theta + sin 3theta+ sin 5 theta + sin 7theta)/(cos theta + cos 3theta + cos 5 theta + cos 7theta) = (tan 3theta + tan theta)/(1 - tan 3theta tan theta) .

(sin 3 theta + sin 5 theta + sin 7 theta + sin 9theta)/(cos 3 theta + cos 5 theta + cos 7 theta + cos 9 theta )=

(sin 3 theta + sin 5 theta + sin 7 theta + sin 9theta)/(cos 3 theta + cos 5 theta + cos 7 theta + cos 9 theta )=

( sin 3 theta + sin 5 theta + sin 7 theta + sin 9 theta)/( cos 3 theta + cos 5 theta + cos 7 theta + cos 9 theta) is equal to

lf 5 cos theta=7 sin theta , find the value of ( sin theta + cos theta)/(2 sin theta -3 cos theta) .

(sin theta + cos theta)/(sin theta - cos theta) + (sin theta - cos theta)/(sin theta + cos theta)= ________