Page No. Date: 11 I prove that : ta...
Question

# Page No. Date: 11 I prove that : tan' , casa lass Itsine EM-X

11th - 12th Class
Maths
Solution
95
4.0 (1 ratings)
( frac{1-sin x}{tan 3 x} ) ( frac{14}{240 frac{1}{4003 x}}-frac{16}{4 rightarrow 0} frac{sin x}{4 sin 3 x} ) ( frac{f t}{2 x-30} frac{3 x}{3 x+2 y^{3} x}-frac{1+}{x rightarrow 0} frac{sin x}{3 x}left{frac{3 x}{4 operatorname{an} 3 x}right. ) ( 1+ ) ( T_{0} ) prove ( tan ^{-1}left(frac{cos x}{1+sin x}right)=frac{pi}{4}-frac{x}{2} ) put ( cos x=cos ^{2} frac{x}{2}-sin ^{2} frac{x}{2}=left(cos left(frac{x}{2}+sin xright)right)left(cos frac{x}{2}-sin frac{x}{2}right. ) ( 1+sin x=left(sin frac{x}{2}+cos frac{x}{2}right)^{2} ) ( ln L cdot operatorname{Hos} tan ^{-1}left(frac{left(cos x+sin frac{x}{2}right)left(cos frac{x-sin x}{2}right)}{left.left(sin frac{x}{2}right)+cos frac{x}{2}right)^{2}}right. ) ( Rightarrow quad operatorname{lan}^{-1}left[frac{cos frac{x}{2}-sin x / 2}{sin frac{x}{2} cos frac{x}{2}+sin frac{x}{2}}right] ) ( Rightarrow quad operatorname{lan}^{-1}left[frac{tan frac{pi}{4}-tan frac{x}{2}}{1+operatorname{ten} frac{pi}{4} tan frac{x}{2}}right] ) ( exists ) ( tan ^{-1}left[tan left(frac{pi}{4}-frac{x}{2}right)right] ) ( E quad frac{pi}{4}-frac{x}{2} quad M cdot P )