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  • Explain solution RD Sharma class 12 chapter Indefinite Integrals exercise 18.8 question 48 maths

Explain solution RD Sharma class 12 chapter Indefinite Integrals exercise 18.8 question 48 maths

Answers (1)

Answer:

        cot\, \theta log\left |\frac{cos\, x}{cos(x+\theta )} \right |+C

Hint:

        tan2x=\frac{2tan\, x}{1-tan^{2}x}

Given:

        \int \! [1+tan\, x\, tan\left | x+\theta \right |]dx                        ...(1)

Explanation:

        tan\, \theta =tan[x+\theta -x]=\frac{tan(x+\theta )-tan\, x}{1+tan\, x\, tan(x+\theta )}

        1+tan\, x\, tan(x+\theta )=cot\, \theta [tan(x+\theta )-tan\, x]

Put in (1)

        \int \! cot\, \theta [tan(x+\theta )-tan\, x]dx

        =cot\, \theta \int \! tan(x+\theta )dx-cot\, \theta \int \! tan\, xdx

        =cot\, \theta [-log\left | cos(x+\theta ) \right |+log\left | cos\, x \right |]+C

        =cot\, \theta log\left |\frac{cos\, x}{cos(x+\theta )} \right |+C

Posted by

Gurleen Kaur

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