If x = a sin theta - b cos theta and y = a co | vedclass

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

Question

(B) Given equations are:$x = a \sin 	heta - b \cos 	heta$ ..... $(1)$$y = a \cos 	heta + b \sin 	heta$ ..... $(2)$Squaring both equations:$x^{2} =

Vedclass · Accepted Answer

$x^{2} + y^{2} = a^{2} + b^{2}$

Vedclass · Answer

(B) Given equations are:$x = a \sin 	heta - b \cos 	heta$ ..... $(1)$$y = a \cos 	heta + b \sin 	heta$ ..... $(2)$Squaring both equations:$x^{2} = (a \sin 	heta - b \cos 	heta)^{2} = a^{2} \sin^{2} 	heta + b^{2} \cos^{2} 	heta - 2ab \sin 	heta \cos 	heta$ ..... $(3)$$y^{2} = (a \cos 	heta + b \sin 	heta)^{2} = a^{2} \cos^{2} 	heta + b^{2} \sin^{2} 	heta + 2ab \sin 	heta \cos 	heta$ ..... $(4)$Adding equations $(3)$ and $(4)$:$x^{2} + y^{2} = a^{2} \sin^{2} 	heta + b^{2} \cos^{2} 	heta - 2ab \sin 	heta \cos 	heta + a^{2} \cos^{2} 	heta + b^{2} \sin^{2} 	heta + 2ab \sin 	heta \cos 	heta$$x^{2} + y^{2} = a^{2} (\sin^{2} 	heta + \cos^{2} 	heta) + b^{2} (\cos^{2} 	heta + \sin^{2} 	heta)$Since $\sin^{2} 	heta + \cos^{2} 	heta = 1$,we get:$x^{2} + y^{2} = a^{2}(1) + b^{2}(1)$$x^{2} + y^{2} = a^{2} + b^{2}$

If $x = a \sin \theta - b \cos \theta$ and $y = a \cos \theta + b \sin \theta$,then which of the following is true?

Similar Questions

The shadow of a tower standing on a level plane is found to be $60\, m$ longer when the angle of elevation of the sun is $30^{\circ}$ than when it is $45^{\circ}$. Find the height of the tower.

The maximum value of $3 \cos \theta + 5 \sin \left( \theta - \frac{\pi}{6} \right)$ for any real value of $\theta$ is

If $\sin \theta + \sin \phi = a$ and $\cos \theta + \cos \phi = b,$ then $\tan \frac{\theta - \phi}{2}$ is equal to

If $\cos(\alpha + \beta) = \frac{3}{5}$,$\sin(\alpha - \beta) = \frac{5}{13}$ and $0 < \alpha, \beta < \frac{\pi}{4}$,then $\tan(2\alpha)$ is equal to

$\frac{1}{4} [\sqrt{3} \cos 23^\circ - \sin 23^\circ] = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module