. Prove that sin
Prove that sin -1x + cos -1x =π / 2 for | x |≤1
Best Answer
Explanation:
For |x|<1, Let -1x=M and -1x=N
sin-1x=A⇒x=sin A.........(1)
sin-1x=B⇒x=cos B......(2)
Comparing (1) & (2) we get,
sinn A = cos B
⇒sinA=sin (90°-B) [By the property of complementary angles]
⇒A=90º-B
⇒A+B=90º
sin-1x+cos-1x=π /2 [π /2=90º]
Thus proved.
Final Answer:
Hence, for |x|<1, it is proved that,sin -1x+cos-1x=π /2.
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