If and , then the value of is…

MATHEMATICS · Subjective · CBSE · Mathematics · Sequences and Series · Sequences and Series

Problem

If 0<cos⁡−1x<10 < \cos^{-1} x < 1 and 1+sin⁡(cos⁡−1x)+sin⁡2(cos⁡−1x)+sin⁡3(cos⁡−1x)+⋯=21 + \sin(\cos^{-1} x) + \sin^2(\cos^{-1} x) + \sin^3(\cos^{-1} x) + \dots = 2 , then the value of 12x212x^2 is .....

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