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

Acetaldehyde forms a white crystalline precipitate on mixing with a ...... solution of

In which of the following reactions,chlorine acts as an oxidising agent?
$(i)$ $CH_3CH_2OH + Cl_2 \longrightarrow CH_3CHO + HCl$
$(ii)$ $CH_3CHO + Cl_2 \longrightarrow CCl_3CHO + HCl$
$(iii)$ $CH_4 + Cl_2 \xrightarrow{hv} CH_3Cl + HCl$
The correct answer is

If the angles of a triangle are in the ratio $1: 1: 4$,then the ratio of the perimeter of the triangle to its largest side is

$A$ distinctive and characteristic functional group in fats is

In a $\triangle ABC$,$\cos \left(\frac{B+2C+3A}{2}\right) + \cos \left(\frac{A-B}{2}\right)$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module