If cos theta - 4 sin theta = 1,then sin theta | vedclass

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

Question

(D) Let $x = \cos 	heta - 4 \sin 	heta = 1$ and $y = \sin 	heta + 4 \cos 	heta$. Squaring both equations and adding them: $x^2 + y^2 = (\cos 	het

Vedclass · Accepted Answer

$\pm 4$

Vedclass · Answer

(D) Let $x = \cos 	heta - 4 \sin 	heta = 1$ and $y = \sin 	heta + 4 \cos 	heta$. Squaring both equations and adding them: $x^2 + y^2 = (\cos 	heta - 4 \sin 	heta)^2 + (\sin 	heta + 4 \cos 	heta)^2$ $x^2 + y^2 = (\cos^2 	heta + 16 \sin^2 	heta - 8 \sin 	heta \cos 	heta) + (\sin^2 	heta + 16 \cos^2 	heta + 8 \sin 	heta \cos 	heta)$ $x^2 + y^2 = \cos^2 	heta + \sin^2 	heta + 16(\sin^2 	heta + \cos^2 	heta)$ $x^2 + y^2 = 1 + 16(1) = 17$ Since $x = 1$,we have $1^2 + y^2 = 17$ $y^2 = 16$ $y = \pm 4$ Therefore,$\sin 	heta + 4 \cos 	heta = \pm 4$.

If $\cos \theta - 4 \sin \theta = 1$,then $\sin \theta + 4 \cos \theta$ is equal to

Similar Questions

If $\sin x + \text{cosec } x = 2$,then $\sin^n x + \text{cosec}^n x$ is equal to

If $\sin \theta + 2 \cos \theta = 1$ and $\theta$ belongs to the $4^{\text{th}}$ quadrant (not lying on the coordinate axes),then $7 \cos \theta + 6 \sin \theta = $

If $\sin 2\theta + \sin 2\phi = 1/2$ and $\cos 2\theta + \cos 2\phi = 3/2$,then $\cos^2(\theta - \phi) = $

The expression $\cos^2 \alpha + \cos^2(\alpha + 120^\circ) + \cos^2(\alpha - 120^\circ)$ is equal to

Let $\alpha$ and $\beta$ be nonzero real numbers such that $2(\cos \beta - \cos \alpha) + \cos \alpha \cos \beta = 1$. Then which of the following is/are true?

Vedclass Test Series

Exam Paper Generator

Online Exam Module