Question

4 sin theta + 8 cos theta =18 find 8 sin theta- 4 cos theta

Answer 1

Answer:

Replacing cosθ=±1−sin2θ−−−−−−−−√cosθ=±1−sin2θ in your equation, 8sinθ=4+cosθ8sin⁡θ=4+cos⁡θ, and considering u=sinθu=sinθ, we have

8u=4±1−u2−−−−−√8u=4±1−u2 which leads to 64u2+16−64u=1−u2→65u2−64u+15=064u2+16−64u=1−u2→65u2−64u+15=0.

Now, you only need to solve this equation to find uu that is sinθsinθ.