Solution: It is better to eliminate the denominator, in order to solve these equations. $\Rightarrow \int \frac{\sin (x-a)}{\sin (x-b)} d x$ Now, add and subtract $b$ in $(x-a)$ $\begin{array}{l}...

Solution: Suppose $\mathrm{I}=\int \frac{\cos 2 x}{(\cos \mathrm{x}+\sin \mathrm{x})^{2}} d x$ On substituting the formula, we obtain $=\int \frac{\cos ^{2} x-\sin ^{2} x}{(\cos x+\sin x)^{2}} d x$...

Solution: First of all we need to convert sec $x$ in terms of $\cos x$ It is known that $\Rightarrow \sec x=\frac{1}{\cos x}, \sec 2 x=\frac{1}{\cos 2 x}$ So, the above equation becomes,...

Solution: Given that, $\int \frac{\sqrt{1-\cos x}}{\sqrt{1+\cos x}} d x$ It is known that $\begin{array}{l} 1-\operatorname{Cos} x=2 \sin ^{2} \frac{x}{2} \\ 1+\cos x=2 \cos ^{2} \frac{x}{2}...

Solution: Given that, $\int \frac{\sqrt{1+\cos 2 x}}{\sqrt{1-\cos 2 x}} d x$ It is known that $\begin{array}{l} 1+\cos 2 x=2 \cos ^{2} x \\ 1-\cos 2 x=2 \sin ^{2} x \end{array}$ On substituting...

Solution: Given that $\int \frac{1}{\sqrt{1-\cos 2 x}} d x$ In the equation given $\cos 2 x=\cos ^{2} x-\sin ^{2} x$ Also it is known that $\cos ^{2} x+\sin ^{2} x=1$ On substituting the values in...