Prove that $\frac{\cos (\pi+x) \cos (-x)}{\sin (\pi-x) \cos \left(\frac{\pi}{2}+x\right)}=\cot ^{2} x$
Prove that $\frac{\cos (\pi+x) \cos (-x)}{\sin (\pi-x) \cos \left(\frac{\pi}{2}+x\right)}=\cot ^{2} x$
$L.H.S.$ $=\frac{\cos (\pi+x) \cos (-x)}{\sin (\pi-x) \cos \left(\frac{\pi}{2}+x\right)}$
$=\frac{[-\cos x][\cos x]}{(\sin x)(-\sin x)}$
$=\frac{-\cos ^{2} x}{-\sin ^{2} x}$
$=\cot ^{2} x$
$= R . H.S$
Similar Questions
The radius of the circle whose arc of length $15\,cm$ makes an angle of $3/4$ radian at the centre is .....$cm$
The radius of the circle whose arc of length $15\,cm$ makes an angle of $3/4$ radian at the centre is .....$cm$
Find the angle in radian through which a pendulum swings if its length is $75\, cm$ and the tip describes an arc of length.
$10 \,cm$
Find the angle in radian through which a pendulum swings if its length is $75\, cm$ and the tip describes an arc of length.
$10 \,cm$
If $\cos \theta = \frac{1}{2}\left( {x + \frac{1}{x}} \right)$, then $\frac{1}{2}\left( {{x^2} + \frac{1}{{{x^2}}}} \right) = $
If $\cos \theta = \frac{1}{2}\left( {x + \frac{1}{x}} \right)$, then $\frac{1}{2}\left( {{x^2} + \frac{1}{{{x^2}}}} \right) = $
If $\cot \,\theta + \tan \theta = m$ and $\sec \theta - \cos \theta = n,$ then which of the following is correct
If $\cot \,\theta + \tan \theta = m$ and $\sec \theta - \cos \theta = n,$ then which of the following is correct
A wheel makes ${360^\circ }$ revolutions in one minute. Through how many radians does it turn in one second?
A wheel makes ${360^\circ }$ revolutions in one minute. Through how many radians does it turn in one second?