Question
$\int \frac{\cos 2 x}{\sin ^2 x} d x$
✓
Answer
$\int \frac{\cos 2 x}{\sin ^2 x} d x$
$=\int \frac{1-2 \sin ^2 x}{\sin ^2 x} d x \quad \ldots \ldots\left[\because \cos 2 \theta=1-2 \sin ^2 \theta\right]$
$=\int\left(\frac{1}{\sin ^2 x}-\frac{2 \sin ^2 x}{\sin ^2 x}\right) d x$
$=\int\left(\operatorname{cosec}^2 x-2\right) d x$
$=-\cot x-2 x + c $
$=\int \frac{1-2 \sin ^2 x}{\sin ^2 x} d x \quad \ldots \ldots\left[\because \cos 2 \theta=1-2 \sin ^2 \theta\right]$
$=\int\left(\frac{1}{\sin ^2 x}-\frac{2 \sin ^2 x}{\sin ^2 x}\right) d x$
$=\int\left(\operatorname{cosec}^2 x-2\right) d x$
$=-\cot x-2 x + c $
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Find $|\bar{u} \times \bar{v}|$ if
i)
→i)
If $\left|\begin{array}{ccc}4+x & 4-x & 4-x \\ 4-x & 4+x & 4-x \\ 4-x & 4-x & 4+x\end{array}\right|=0$, then find the values of $x$.
→$\bar{a} \cdot(\bar{b}+\bar{c})$
→Show that the function $f(x) = x^3 + 10x + 7$ for $x \in R$ is strictly increasing
→Construct a $3 \times 4$ matrix $A = [a_{ij}]$ whose element $a_{ij}$ are given by:
$a_{ij} = i - j$
→$a_{ij} = i - j$
Determine the order and degree of the following differential equations:
→$\frac{d y}{d x}=3 y+\sqrt[4]{1+5\left(\frac{d y}{d x}\right)^2}$
Show that $f(x) = x –\cos x$ is increasing for all $x.$
→Write the negations of the following :$\sqrt{2}$ is a rational number.
→If $A=\left[\begin{array}{lll}1 & 2 & 3 \\ 1 & 1 & 5 \\ 2 & 4 & 7\end{array}\right]$, then find the value of $a_{31} A_{31}+a_{32} A_{32}+a_{33} A_{33}$
→Evaluate $\int\frac{1-\sin\text{x}}{\cos^2\text{x}}\text{ dx}$
→