If left| {cos ,theta ,left{ {sin theta + sqrt | vedclass

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

Question

(b) Let $u = \cos 	heta \left\{ {\sin 	heta + \sqrt {{{\sin }^2}	heta + {{\sin }^2}\alpha } } ight\}$

==> ${(u - \sin 	heta \cos 	heta )^

Vedclass · Accepted Answer

$\sqrt {1 + {{\sin }^2}\alpha } $

Vedclass · Answer

(b) Let $u = \cos 	heta \left\{ {\sin 	heta + \sqrt {{{\sin }^2}	heta + {{\sin }^2}\alpha } } ight\}$

==> ${(u - \sin 	heta \cos 	heta )^2} = {\cos ^2}	heta ({\sin ^2}	heta + {\sin ^2}\alpha )$ 

==> ${u^2}{	an ^2}	heta - 2u	an 	heta + {u^2} - {\sin ^2}\alpha = 0$ 

Since tan $	heta $ is real, therefore 

==> $4{u^2} - 4{u^2}({u^2} - {\sin ^2}\alpha ) \ge 0$

$ \Rightarrow {u^2} - (1 + {\sin ^2}\alpha ) \le 0$ 

==> $|u|\, \le \sqrt {1 + {{\sin }^2}\alpha } $.

If $\left| {\cos \,\theta \,\left\{ {\sin \theta + \sqrt {{{\sin }^2}\theta + {{\sin }^2}\alpha } } \right\}\,} \right|\, \le k,$ then the value of $k$ is

Similar Questions

If $\sin (\alpha - \beta ) = \frac{1}{2}$ and $\cos (\alpha + \beta ) = \frac{1}{2},$ where $\alpha $ and $\beta $ are positive acute angles, then

The value of $k$, for which ${(\cos x + \sin x)^2} + k\,\sin x\cos x - 1 = 0$ is an identity, is

If $\cos x=-\frac{3}{5}, x$ lies in the third quadrant, find the values of other five trigonometric functions.

Find the value of the trigonometric function $\sin \left(-\frac{11 \pi}{3}\right)$

The value of $\cos A - \sin A$ when $A = \frac{{5\pi }}{4},$ is