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Question

If for the function f(x)=cos1(x21+x2) the range is (a,b), then find sin(b).

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Solution

Consider f(θ)=cos1(θ)
Then θϵ[1,1]

Similarly in the above case
1x21+x21

Now x21+x2 will always be greater than 0.

Hence, 0x21+x21

x21+x2ϵ[0,1]

Hence, cos1(x21+x2)ϵ[0,π2]

f(x)ϵ[0,π2]

Hence a=0 and b=π2

Therefore sinb=sin(π2)=1.

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