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If (sin –1 x ) 2 – (cos –1 x ) 2 = a ;0 < x < 1; a \(\neq\)0, then the value of 2 x 2 – 1 is [JEE Main 2021, 27 Au…

If (sin^–1 x)² – (cos^–1 x)² = a;0 < x < 1;a \(\neq\)0, then the value of 2x² – 1 is

[JEE Main 2021, 27 Aug (Shift 1)]

\( \cos \left(\frac{4 \mathrm{a}}{\pi}\right) \)

\( \sin \left(\frac{2 \mathrm{a}}{\pi}\right) \)

\( \cos \left(\frac{2 \mathrm{a}}{\pi}\right) \)

\( \sin \left(\frac{4 \mathrm{a}}{\pi}\right) \)

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If (sin –1 x ) 2 – (cos –1 x ) 2 = a ;0 &lt; x &lt; 1; a \(\neq\)0, then the value of 2 x 2 – 1 is [JEE Main 2021, 27 Au…