Which of the following is the solution set of the equation $$sin$$−$$1$$⁡$$x=$$$$cos$$−$$1$$⁡$$x+$$$$sin$$−$$1$$⁡(3x$$−$$1)?

Question

Which of the following is the solution set of the equation $$sin$$−$$1$$⁡$$x=$$$$cos$$−$$1$$⁡$$x+$$$$sin$$−$$1$$⁡(3x$$−$$1)?

Infinity Learn · Accepted Answer

For the existence of the  given equation, we must have−$$1$$≤x≤$$1$$ and −$$1$$≤$$3x$$−$$1$$≤$$1$$⇒$$0$$≤x≤$$23Now$$,$$sin$$−$$1$$⁡$$x=$$$$cos$$−$$1$$⁡$$x+$$$$sin$$−$$1$$⁡(3x$$−$$1)⇒ $$sin$$−$$1$$⁡x−$$cos$$−$$1$$⁡$$x=$$$$sin$$−$$1$$⁡(3x$$−$$1)⇒ $$2sin$$−$$1$$⁡x−π$$2=$$$$sin$$−$$1$$⁡(3x$$−$$1)⇒    $$sin$$⁡$$2sin$$−$$1$$⁡x−π$$2=$$$$sin$$⁡$$sin$$−$$1$$⁡(3x$$−$$1)⇒    −$$cos$$⁡$$2sin$$−$$1$$⁡$$x=3x$$−$$1$$⇒    −$$1$$−$$2sin2$$⁡$$sin$$−$$1$$⁡$$x=3x$$−$$1$$⇒    −$$1$$−$$2x2=3x$$−$$1$$⇒    $$2x2$$−$$3x=0$$⇒$$x=0$$,$$32$$⇒$$x=0$$                         [∵$$0$$≤x≤$$2/3$$]

Which of the following is the solution set of the equation $\sin^{- 1} x = \cos^{- 1} x + \sin^{- 1} (3 x - 1) ?$

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Which of the following is the solution set of the equation sin−1⁡x=cos−1⁡x+sin−1⁡(3x−1)?

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Which of the following is the solution set of the equation $\sin^{- 1} x = \cos^{- 1} x + \sin^{- 1} (3 x - 1) ?$