Question

sin^-1x+ sin ^-1 1/2+cos ^-1x+cos^-1 1/2​

Answer 1

Answer:

si

n−1x+cos−1(1−x)=sin−1(−x)sin−1x+cos−1(1−x)=sin−1(−x)

⇒cos−1(1−x)=sin−1(x)−sin−1(−x)⇒cos−1(1−x)=sin−1(x)−sin−1(−x) 

⇒cos−1(1−x)=−2sin−1x⇒cos−1(1−x)=−2sin−1x

⇒1−x=cos(−2sin−1x)⇒1−x=cos(−2sin−1x) 

=cos(2sin−1x)=1−2sin2(sin−1x)=1−2x2=cos(2sin−1x)=1−2sin2(sin−1x)=1−2x2

⇒⇒ Either x=0x=0 or x=1/2x=1/2

But x=1/2x=1/2 does not satisfy the given equation 

∴x=0

Answer 2

Answer:

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