If cos θ = - 3 2 and sin α = - 3 5 , where θ does not lie in the third quadrant, then 2 tan α + 3 tan θ cot 2 θ + cos α is equal to

Step-by-step solution

Given, cos θ = - 3 2 < 0 and θ does not lie in third quadrant. ∴   θ must be lying in 2 n d quadrant. ⇒   tan θ = - 1 3 and cot θ = - 3     . . . ( i ) As, sin α = - 3 5 , thus α lies in 3 r d or 4 t h quadrant. If α is in third quadrant, then tan α = 3 4 and cos α = - 4 5 . ∴   2 tan α + 3 tan θ cot 2 θ + cos α = 2 · 3 4 - 3 · 1 3 3 - 4 5 = 3 2 - 1 3 - 4 5 = 5 22 . If α is in fourth q