For,x∈$$12$$,$$1$$,$$sin$$−$$13x$$−$$4x3=$$

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Infinity Learn · Accepted Answer

Let $$x=$$$$sin$$θ.  Since x∈$$12$$,$$1$$, ⇒$$sin$$θ∈$$12$$,$$1$$ ⇒π$$6$$≤θ≤π$$2$$ ⇒π$$2$$≤$$3$$θ≤$$3$$$$π$$$$2$$ ⇒$$-3$$$$π$$$$2$$≤$$-3$$θ≤$$-$$π$$2$$ ⇒π$$-3$$$$π$$$$2$$≤π$$-3$$θ≤π$$-$$π$$2$$ ⇒$$-$$π$$2$$≤π$$-3$$θ≤π$$2$$ Now $$sin$$$$-13x-4x3=$$$$sin$$$$-13sin$$θ$$-4sin3$$θ                                      $$=$$$$sin$$$$-1sin3$$θ                                      $$=$$$$sin$$$$-1sin$$π$$-3$$θ                                       $$=$$π$$-3$$θ                                        $$=$$π$$-3sin-1x$$

For, $x \in [\frac{1}{2}, 1], \sin^{- 1} (3 x - 4 x^{3}) =$

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For,x∈12,1,sin−13x−4x3=

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For, $x \in [\frac{1}{2}, 1], \sin^{- 1} (3 x - 4 x^{3}) =$