If $\tan \theta = \frac{{ - 4}}{3},$ then $\sin \theta = $

If ${\tan ^2}\alpha {\tan ^2}\beta + {\tan ^2}\beta {\tan ^2}\gamma + {\tan ^2}\gamma {\tan ^2}\alpha $$ + 2{\tan ^2}\alpha {\tan ^2}\beta {\tan ^2}\gamma = 1,$ then the value of ${\sin ^2}\alpha + {\sin ^2}\beta + {\sin ^2}\gamma $ is

Find the radius of the circle in which a central angle of $60^{\circ}$ intercepts an arc of length $37.4 \,cm$ ( use $\pi=\frac{22}{7}$ ).

The equation ${\sin ^2}\theta  = \frac{{{x^2} + {y^2}}}{{2xy}},x,y, \ne 0$ is possible if

Prove that $\cos \left(\frac{3 \pi}{4}+x\right)-\cos \left(\frac{3 \pi}{4}-x\right)=-\sqrt{2} \sin x$

$\frac{{2\sin \theta \,\tan \theta (1 - \tan \theta ) + 2\sin \theta {{\sec }^2}\theta }}{{{{(1 + \tan \theta )}^2}}} = $