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Question: The number of solution of the equation \(\sin^{2}\theta - \sin\theta - 2 = 0\), are....

The number of solution of the equation sin⁡2θ−sin⁡θ−2=0\sin^{2}\theta - \sin\theta - 2 = 0, are.

A

No solution

B

One solution

C

Two solutions

D

Infinitely many solutions

Answer

No solution

Explanation

Solution

We know cos⥂ecθ=54,43\text{cos} ⥂ \text{ec}\theta = \frac{5}{4},\frac{4}{3}, (using A.M. sin⁡θ=45,34\sin\theta = \frac{4}{5},\frac{3}{4} G.M.)
But since ∣sin⁡2x∣|\sin 2x|

So, there does not exist any solution.