If 3 cos x neq 2 sin x,then the general solut | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Given equation: $\sin^2 x - \cos 2x = 2 - \sin 2x$ Using identities $\cos 2x = 1 - 2\sin^2 x$ and $\sin 2x = 2\sin x \cos x$: $\sin^2 x - (1 - 2\s

Vedclass · Accepted Answer

$(4n \pm 1) \frac{\pi}{2}, n \in \mathbb{Z}$

Vedclass · Answer

(C) Given equation: $\sin^2 x - \cos 2x = 2 - \sin 2x$ Using identities $\cos 2x = 1 - 2\sin^2 x$ and $\sin 2x = 2\sin x \cos x$: $\sin^2 x - (1 - 2\sin^2 x) = 2 - 2\sin x \cos x$ $3\sin^2 x - 1 = 2 - 2\sin x \cos x$ Alternatively,using $\sin^2 x = 1 - \cos^2 x$ and $\cos 2x = 2\cos^2 x - 1$: $(1 - \cos^2 x) - (2\cos^2 x - 1) = 2 - 2\sin x \cos x$ $2 - 3\cos^2 x = 2 - 2\sin x \cos x$ $-3\cos^2 x + 2\sin x \cos x = 0$ $\cos x (2\sin x - 3\cos x) = 0$ Since $3\cos x 
eq 2\sin x$,we have $2\sin x - 3\cos x 
eq 0$. Therefore,$\cos x = 0$. The general solution for $\cos x = 0$ is $x = (2n + 1) \frac{\pi}{2}$,which can be written as $x = (4n \pm 1) \frac{\pi}{2}$ for $n \in \mathbb{Z}$.

If $3 \cos x \neq 2 \sin x$,then the general solution of $\sin^2 x - \cos 2x = 2 - \sin 2x$ is

Similar Questions

When $20 \ g$ of naphthoic acid $(C_{11}H_8O_2)$ is dissolved in $50 \ g$ of benzene $(K_f = 1.72 \ K \ kg \ mol^{-1})$,a freezing point depression of $2 \ K$ is observed. The Van't Hoff factor $(i)$ is:

Which of the following is a cationic detergent?

If $n(A) = 3$ and $n(B) = 6$ and $A \subseteq B$,then the number of elements in $A \cap B$ is equal to

If $k > 1$ and the determinant of the matrix $A^2$,where $A = \begin{bmatrix} k & k\alpha & \alpha \\ 0 & \alpha & k\alpha \\ 0 & 0 & k \end{bmatrix}$,is $k^2$,then $|\alpha|$ is equal to

Which of the following options is correct for an object having a straight-line motion represented by the following graph?

Vedclass Test Series

Exam Paper Generator

Online Exam Module