Question

if 8 sin theta =4+cos thetA,find the value of tan theta​

Answer 1

Answer:

8sinθ=4+cosθ.

⇒64sin2θ=(4+cosθ)2=16+8cosθ+cos2θ.

⇒16+8cosθ+cos2θ=64(1−cos2θ)=64−64cos2θ.

⇒65cos2θ+8cosθ−48=0.

⇒(5cosθ−4)(13cosθ+12)=0.

⇒cosθ=45 or cosθ=−1213.

If cosθ=45,sinθ=4+cosθ8=35⇒tanθ=34.

If cosθ=−1213,sinθ=4+cosθ8=513⇒tanθ=−512.

⇒tanθ=34 or tanθ=−512.