Let be any real number such that

MATHEMATICS · Multi-part · CBSE · Mathematics · Inverse Trigonometric Functions · Inverse Trigonometric Functions

Problem

Let xx be any real number such that ∣x∣≤12|x|\le \tfrac12. Consider the composite function S(x)=sin⁡(arccos⁡(2x))S(x)=\sin\bigl(\arccos(2x)\bigr). (i) Simplify S(x)S(x) to an expression involving only xx, without any inverse trigonometric or radical signs in the final numerator. (ii) Hence find the exact value of S(14)S\bigl(\tfrac14\bigr).

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