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Question : 196 of 200
Marks:
+1,
-0
Solution:
We have
sin‌−1x−cos−1x=‌Let
A=sin‌−1x⇒x=sin‌A,cos‌A=√1−x2‌ and ‌‌B=cos−1x⇒x=cos‌B,sin‌B=√1−x2Now,
sin‌(A−B)‌=sin‌A‌cos‌B−cos‌A‌s‌i‌n‌B‌=x⋅x−√1−x2⋅√1−x2‌=x2−1+x2sin‌(‌)‌=2x2−1⇒2x2−1‌=‌⇒2x2=‌⇒x2=‌⇒‌‌x‌=‌
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