The number of solutions of tan, (5pi, cos, th | vedclass

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

Question

$tan \,(5\pi \,cos\, 	heta ) = cot\, (5 \pi\, sin\, 	heta )$

$tan \,(5\pi \,cos\, 	heta ) = tan\, \left( {\frac{\pi }{2}\, - \,5\pi \sin 	heta

Vedclass · Accepted Answer

$28$

Vedclass · Answer

$tan \,(5\pi \,cos\, 	heta ) = cot\, (5 \pi\, sin\, 	heta )$

$tan \,(5\pi \,cos\, 	heta ) = tan\, \left( {\frac{\pi }{2}\, - \,5\pi \sin 	heta } ight)$

$5\pi \,cos	heta = n\pi + \pi /2 - 5\pi \,sin	heta$

$(cos	heta + sin	heta ) = \left( {\frac{{2n + 1}}{{10}}} ight)$

$\Rightarrow -1 < \frac{{2n + 1}}{{10\sqrt 2 }} < 1$ 

$\Rightarrow$ $ - \,\frac{{10\sqrt 2 \, - 1}}{2}$ $< n <$ $\frac{{10\sqrt 2 \, - 1}}{2}$

$	herefore$ $n= 14$ for each $&lsquo;n&rsquo;$ there are two values of $	heta$

no. of solutions $= 28$

The number of solutions of $tan\, (5\pi\, cos\, \theta ) = cot (5 \pi \,sin\, \theta )$ for $\theta$ in $(0, 2\pi )$ is :

Similar Questions

The number of solutions of the equation $\sin x=$ $\cos ^{2} x$ in the interval $(0,10)$ is

The number of solutions of the equation $\sqrt[3]{{\sin \theta - 1}} + \sqrt[3]{{\sin \theta }} + \sqrt[3]{{\sin \theta + 1}} = 0$ in $[0,4\pi]$ is

The number of solutions of the equation $\sin \theta+\cos \theta=\sin 2 \theta$ in the interval $[-\pi, \pi]$ is

Find the general solution of the equation $\sec ^{2} 2 x=1-\tan 2 x$

The number of solutions of the equation $x +2 \tan x =\frac{\pi}{2}$ in the interval $[0,2 \pi]$ is :