EXAMPLE 27 Prove that tan -1 X
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EXAMPLE 27 Prove that tan -1 X
11th - 12th Class
Maths
Solution
126
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SOLUTION We have [ mathrm{LHS}=tan ^{-1}left(frac{cos x-sin x}{cos x+sin x}right) ] ( =tan ^{-1}left(frac{1-tan x}{1+tan x}right)[text { dividing num. and denom. by } cos x] ) [ begin{aligned} &=tan ^{-1}left{tan left(frac{pi}{4}-xright)right}=left(frac{pi}{4}-xright)=mathrm{RHS} therefore tan ^{-1}left(frac{cos x-sin x}{cos x+sin x}right) &=left(frac{pi}{4}-xright) end{aligned} ]

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