(3) 2 tan-(sin x) = tan-'(2 sec x) ...
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(3) 2 tan-(sin x) = tan-'(2 sec x) 0
JEE/Engineering Exams
Maths
Solution
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( because quad 2 tan ^{-1}(sin x)=tan ^{-1}(2 sec x) ) ( left[begin{array}{ll}therefore & left.2 tan ^{-1} x=tan ^{-1} frac{2 x}{1-x^{2}}right] operatorname{sos} tan ^{-1}left(frac{2 sin x}{1-sin ^{2} x}right) & =tan ^{-1}(2 sec x)end{array}right. ) ( Rightarrow quad frac{2 sin x}{cos ^{2} x}=2 sec x ) ( Rightarrowleft[begin{array}{ll}therefore & sin ^{2} x+cos ^{2} x=1end{array}right] ) ( Rightarrow quad frac{2 sin x}{cos x} cdot frac{1}{cos x}= ) ( x=1 ) ( begin{aligned} 2 tan x cdot sec x &=x sec x tan x &=1 end{aligned} ) ( S_{0}, quad x=pi / 4 quad[-0

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