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  • Need solution for rd sharma maths class 12 chapter Indefinite Integrals exercise 18.2 question 25

Need solution for rd sharma maths class 12 chapter Indefinite Integrals exercise 18.2 question 25

Answers (1)

best_answer

\tan x-\cot x+c

Hint:To solve this equation we use \int \tan x; tan^{2}x formula

\begin{aligned} &\text { Given: } \int(\tan x+\cot x)^{2} d x \\ &\text { Solution: } \int(\tan x+\cot x)^{2} d x \\ &(a+b)^{2}=a^{2}+b^{2}+2 a b \\ &=\int \tan ^{2} x+\cot ^{2} x+2 \tan x \cot x d x \\ &=\int \tan ^{2} x+\cot ^{2} x+2 \frac{1}{\cot x} \cot x d x \quad\left[\tan x=\frac{1}{\cot x}\right] \end{aligned}\begin{aligned} &=\int( \sec ^{2} x-1+\cos e c^{2} x-1+2)dx+c \quad\left[\begin{array}{l} \tan ^{2} x=\sec ^{2} x-1 \\ \operatorname{cosec}^{2} x=\cot ^{2} x-1 \end{array}\right] \\ &=\int \sec ^{2} x d x+\int \cos e c^{2} x d x \quad\left[\begin{array}{l} \int \sec ^{2} x d x=\tan x+c \\ \int \operatorname{cosec}^{2} x d x=\cot x+c \end{array}\right] \\ &=\tan x-\cot x+c \end{aligned}

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