If 2sin theta + tan theta = 0,then the genera | vedclass

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

Question

(B) Given the equation: $2\sin 	heta + 	an 	heta = 0$We can write $	an 	heta$ as $\frac{\sin 	heta}{\cos 	heta}$:$2\sin 	heta + \frac{\sin 	h

Vedclass · Accepted Answer

$n\pi, 2n\pi \pm \frac{2\pi}{3}$

Vedclass · Answer

(B) Given the equation: $2\sin 	heta + 	an 	heta = 0$We can write $	an 	heta$ as $\frac{\sin 	heta}{\cos 	heta}$:$2\sin 	heta + \frac{\sin 	heta}{\cos 	heta} = 0$Factor out $\sin 	heta$:$\sin 	heta \left( 2 + \frac{1}{\cos 	heta} ight) = 0$This gives two cases:Case $1$: $\sin 	heta = 0 \Rightarrow 	heta = n\pi$,where $n \in \mathbb{Z}$.Case $2$: $2 + \frac{1}{\cos 	heta} = 0$ $\Rightarrow \frac{1}{\cos 	heta} = -2$ $\Rightarrow \cos 	heta = -\frac{1}{2}$.Since $\cos 	heta = -\frac{1}{2} = \cos \left( \frac{2\pi}{3} ight)$,the general solution is $	heta = 2n\pi \pm \frac{2\pi}{3}$,where $n \in \mathbb{Z}$.Combining both cases,the general values of $	heta$ are $n\pi$ and $2n\pi \pm \frac{2\pi}{3}$.

If $2\sin \theta + \tan \theta = 0$,then the general values of $\theta$ are

Similar Questions

The number of elements in the set $\{x \in [0, 180^{\circ}] : \tan(x+100^{\circ}) = \tan(x+50^{\circ}) \tan x \tan(x-50^{\circ})\}$ is . . . . . . .

If $\sin \left(5 x+\frac{\pi}{4}\right)=0$,then $x$ is equal to

If $5 \cos 2 \theta + 2 \cos^2 \frac{\theta}{2} + 1 = 0$, where $0 < \theta < \pi$, then the values of $\theta$ are:

If $f(x)=\cos^2 x+\cos^2 2x+\cos^2 3x$,then the number of values of $x \in [0, 2\pi]$ for which $f(x)=1$ is

Solve $2 \cos^{2} x + 3 \sin x = 0$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module