Find the number of solutions of equation sin -1(4 sin 2 θ+ sin θ)+ cos -1(-1+6 sin θ)=(π/2), in θ ∈[0,5 π].

Question

Find the number of solutions of equation sin -1(4 sin 2 θ+ sin θ)+ cos -1(-1+6 sin θ)=(π/2), in θ ∈[0,5 π]. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

We must have, 4 sin 2 θ+ sin θ=-1+6 sin θ ⇒ sin θ=1, (1/4) ⇒ 6 solutions. ]

Q. Find the number of solutions of equation $sin^{- 1} (4 sin^{2} θ + sin θ) + cos^{- 1} (- 1 + 6 sin θ) = \frac{π}{2}$ , in $θ \in [0, 5 π]$ .