-COS X EXAMPLE 26 Prove that tan 1 ...
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-COS X EXAMPLE 26 Prove that tan 1 + cos x)

11th - 12th Class
Maths
Solution
80
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We have [ begin{array}{l} begin{aligned} mathrm{LHS} &=tan ^{-1}(sqrt{frac{1-cos x}{1+cos x}})=tan ^{-1} sqrt{frac{2 sin ^{2}left(frac{x}{2}right)}{2 cos ^{2}left(frac{x}{2}right)}} &=tan ^{-1}left(tan frac{x}{2}right)=frac{x}{2}=mathrm{RHS} end{aligned} therefore tan ^{-1}(sqrt{frac{1-cos x}{1+cos x}})=frac{x}{2} end{array} ]
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