How do you simplify $cos (arcsin (2 x^{3}))$ $Cos(arcsin (2x^3))$ ?

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How do you simplify $cos (arcsin (2 x^{3}))$ $Cos(arcsin (2x^3))$ ?

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Answer 1 · 2016-07-05T09:06:06

reqd. value $= \sqrt{1 - 4 x^{6}}$ $=sqrt(1-4x^6)$

Explanation:

Suppose that $arcsin (2 x^{3}) = θ$ $arcsin(2x^3)=theta$ , so that, by defn. of $arcsin, sin θ = 2 x^{3}$ $arcsin, sintheta=2x^3$

Now, reqd. value $= cos (arcsin 2 x^{3}) = cos θ = \sqrt{1 - {sin}^{2} θ} = \sqrt{1 - {(2 x^{3})}^{2}} = \sqrt{1 - 4 x^{6}}$ $=cos(arcsin2x^3)= costheta = sqrt (1-sin^2theta) = sqrt{1-(2x^3)^2}=sqrt(1-4x^6)$ .

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How do you simplify $cos (arcsin (2 x^{3}))$ $Cos(arcsin (2x^3))$ ?

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How do you simplify $cos (arcsin (2 x^{3}))$ $Cos(arcsin (2x^3))$ ?