If a cos theta + b sin theta = m and a sin th | vedclass

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

Question

(C) Given that $a \cos 	heta + b \sin 	heta = m$ $(1)$ and $a \sin 	heta - b \cos 	heta = n$ $(2)$ Squaring both equations and adding them,we get:

Vedclass · Accepted Answer

${m^2} + {n^2}$

Vedclass · Answer

(C) Given that $a \cos 	heta + b \sin 	heta = m$ $(1)$ and $a \sin 	heta - b \cos 	heta = n$ $(2)$ Squaring both equations and adding them,we get: $(a \cos 	heta + b \sin 	heta)^2 + (a \sin 	heta - b \cos 	heta)^2 = m^2 + n^2$ Expanding the squares: $(a^2 \cos^2 	heta + b^2 \sin^2 	heta + 2ab \sin 	heta \cos 	heta) + (a^2 \sin^2 	heta + b^2 \cos^2 	heta - 2ab \sin 	heta \cos 	heta) = m^2 + n^2$ Grouping the terms: $a^2(\cos^2 	heta + \sin^2 	heta) + b^2(\sin^2 	heta + \cos^2 	heta) = m^2 + n^2$ Since $\sin^2 	heta + \cos^2 	heta = 1$,we have: $a^2(1) + b^2(1) = m^2 + n^2$ Therefore,$a^2 + b^2 = m^2 + n^2$.

If $a \cos \theta + b \sin \theta = m$ and $a \sin \theta - b \cos \theta = n,$ then ${a^2} + {b^2} = $

Similar Questions

If $\cos x = \tan y$,$\cot y = \tan z$ and $\cot z = \tan x$,then $\sin x$ equals to

If $a = \sin \frac{\pi}{18} \sin \frac{5\pi}{18} \sin \frac{7\pi}{18}$ and $x$ is the solution of the equations $y = 2[x] + 2$ and $y = 3[x - 2]$,where $[x]$ denotes the greatest integer function of $x$,then $a$ is equal to:

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

Let $P(\alpha, \beta)$ and $Q(\gamma, \delta)$ be two points that lie on the curve $\tan^2(x+y) + \cos^2(x+y) + y^2 + 2y = 0$ in the $XY$-plane. If the distance between $P$ and $Q$ is $d$,then $\cos d =$

$\operatorname{cosec} 48^{\circ}+\operatorname{cosec} 96^{\circ}+\operatorname{cosec} 192^{\circ}+\operatorname{cosec} 384^{\circ}=$

Vedclass Test Series

Exam Paper Generator

Online Exam Module