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Solution


Q.

Let the inverse trigonometric functions take principal values. The number of real solutions of the equation 2sin-1x+3cos-1x=2π5, is _____.    [2024]

Ans.

(0)

We have, 2sin-1x+3cos-1x=2π5

⇒2(π2-cos-1x)+3cos-1x=2π5

⇒π+cos-1x=2π5 ⇒ cos-1x=-3π5

Which is not possible as cos-1x∈[0,π]

∴No solution exists.