If (a$$ < $$0) and x ∈ $$($$– a, $$a)$$, then $$tan$$−$$1$$⁡$$xa2$$−$$x2=$$

Correct option is 1−sin−1⁡xa

Questions

If (a < 0) and x ∈ (– a, a), then $\tan^{- 1} (\frac{x}{\sqrt{a^{2} - x^{2}}}) =$

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−sin−1⁡xa

sin−1⁡xa

cos−1⁡xa

none of these

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detailed solution

Correct option is A

Put x = a sin θ, then the given expression=tan−1⁡asin⁡θ−acos⁡θ (∵a<0)=tan−1⁡(−tan⁡θ)=−θ=−sin−1⁡xa

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If (a < 0) and x ∈ (– a, a), then tan−1⁡xa2−x2=

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

If (a < 0) and x ∈ (– a, a), then $\tan^{- 1} (\frac{x}{\sqrt{a^{2} - x^{2}}}) =$