Introduction to...

If $$\sin A, \cos A$$ and $$\tan A$$ are in $$G.P.,$$ then $$\cot^6 A- \cot^2A$$ is equal to

If $$\displaystyle x=r\sin \theta \cdot \cos \phi,$$  $$y=r\sin \theta \cdot \sin \phi$$ and $$\displaystyle z= r\cos \theta$$, then the value of $$\displaystyle x^{2}+y^{2}+z^{2}$$ is independent of: 

If $$\sin { A } =a\cos { B } $$ and $$\cos { A } =b\sin { B } $$, then $$\left( { a }^{ 2 }-1 \right) \tan ^{ 2 }{ A } +\left( 1-{ b }^{ 2 } \right) \tan ^{ 2 }{ B } $$   is equal to

If $$\tan A+\cot A=4$$, then $$\tan^2A+\cot^2A$$ is equal to

If $$\displaystyle a\sec \alpha - c\tan \alpha =d$$ and $$\displaystyle b\sec \alpha -d\tan \alpha =c$$  $$\ \ \  then$$

If $$\displaystyle \frac{2\sin \alpha }{1+\sin \alpha +\cos \alpha }=\lambda$$ then $$\displaystyle \frac{1+\sin \alpha -\cos \alpha }{1+\sin \alpha }$$ is equal to

If $$\displaystyle  \sin\theta + cosec \theta= 2,$$  then the value of $$\displaystyle \sin ^{8}\theta + cosec ^{8}\theta$$ is equal to

If $$\displaystyle \frac{\sin A}{\sin B}= \frac{\sqrt{3}}{2}$$and $$\displaystyle \frac{\cos A}{\cos B}= \frac{\sqrt{5}}{2},0< A,  B< \dfrac{\pi}{2},$$ then find the value of $$\displaystyle \tan A+\tan B$$

If $$\displaystyle 5\tan\theta = 4 $$ then $$\displaystyle \frac{5\sin \theta -3\cos \theta }{5\sin \theta +2\cos \theta }$$ is equal to

If $$\displaystyle \sin x=2\cos y,\sqrt 6 \sin y=\tan z$$ and $$\displaystyle 2\sin z=\sqrt 3 \cos x,u,v,w $$ denotes, respectively,$$\displaystyle \sin ^{2}x, \sin ^{2}y, \sin ^{2}z,$$ then the value of $$u+v+w$$  is