- Home
- Standard 11
- Mathematics
3.Trigonometrical Ratios, Functions and Identities
medium
यदि $2y\,\cos \theta = x\sin \,\theta {\rm{ and }}2x\sec \theta - y\,{\rm{cosec}}\,\theta = 3,$ तो ${x^2} + 4{y^2} = $
A
$4$
B
$-4$
C
$± 4$
D
इनमें से कोई नहीं
Solution
(a) दिया है $2y\,\,\cos \theta = x\,\sin \theta $…..$(i)$
एवं $2x\,\sec \theta – y\,\,{\rm{cosec}}\,\theta = 3$…..$(ii)$
$ \Rightarrow \,\,\frac{{2x}}{{\cos \theta }} – \frac{y}{{\sin \theta }} = 3$
$ \Rightarrow \,\,2x\,\sin \theta – y\,\cos \theta – 3\,\sin \theta \cos \theta = 0$…..$(iii)$
$(i)$ व $(iii)$ को हल करने पर,
$y = \sin \theta $ एवं $x = 2\,\,\cos \theta $
अब, ${x^2} + 4{y^2} = 4\,\,{\cos ^2}\theta + 4\,\,{\sin ^2}\theta $
$ = 4\,({\cos ^2}\theta + {\sin ^2}\theta ) = 4$.
Standard 11
Mathematics
