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Question

If the range of functions f(x)=(cos1x3)2+πsin1x3(sin1x3)2+π24(x2+2x+1) is [a,b]. then the value of ba is

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Solution

Let sin1(x3)=t and g(x)=(cos1x3)2+πsin1x3(sin1x3)2
g(x)=(π2t)2+πtt2g(x)=π24f(x)=π24((x+1)2+1)

Now
1x313x32x+140(x+1)2161(x+1)2+117π24π24((x+1)2+1)17π24

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