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  • Need solution for rd sharma maths class 12 chapter Indefinite Integrals exercise 18.2 question 28

Need solution for rd sharma maths class 12 chapter Indefinite Integrals exercise 18.2 question 28

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\frac{1}{\sqrt{2}}x+c

Hint: To solve this equation we use 2 \cos 2x and \cos 2x formula

\begin{aligned} &\text { Given: } \int \frac{\cos ^{2} x-\sin ^{2} x}{\sqrt{1+\cos 4 x}} d x \\ &\text { Solution: } \frac{\cos 2 x}{\sqrt{2 \cos ^{2} 2 x}} d x \quad\left[\begin{array}{l} \cos ^{2} x-\sin ^{2} x=\cos 2 x \\ 1+\cos 4 x=2 \cos ^{2}2 x \end{array}\right] \\ &=\frac{1}{\sqrt{2}}\left(\frac{\cos 2 x}{\cos 2 x}\right) \\ &=\frac{1}{\sqrt{2}} \\ &\int \frac{\cos ^{2} x-\sin ^{2} x}{\sqrt{1+\cos 4 x}} d x=\int \frac{1}{\sqrt{2}} d x \\ &=\frac{1}{\sqrt{2}} x+c \end{aligned}

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