Introduction to...

Given $$a = \sec^{2} \alpha ,b=\mathrm{cosec}^{2} \alpha , and ,  c=\dfrac{1}{1-\sin^{2}\alpha \cos^{2}\alpha }.$$ The value of $$bc + ca - ab$$ is

lf $$\sin\alpha=a\sin\beta$$ and $$\cos\alpha=b\cos\beta$$ , then $$\tan\alpha$$=

 If $$\sin\mathrm{x}+\sin^{2}\mathrm{x}=1$$, then $$\cos^{12}\mathrm{x}+3\cos^{10}\mathrm{x}+3\cos^{8}\mathrm{x}+\cos^{6}\mathrm{x}+2\cos^{4}\mathrm{x}+\cos^{2}\mathrm{x}-2$$ is equal to 

If $$\sin {x}+\sin^{2}{x}+\sin^{3}{x}=1 ,\ \ then \ \  \cos^{6}{x}-4\cos^{4}{x}
+8\cos^{2}{x}$$ is equal to

If $$\sin\alpha+\cos\alpha=m, m^{2}\leq 2$$, then $$\sin^{6}\alpha+\cos^{6}\alpha=$$

If $$a \sin^{2}\theta+b\cos^{2}\theta=a\cos^{2}\phi+b\sin^{2}\phi=1$$ and $$a \tan\theta=b\tan\phi$$, then choose the correct option.

The value of the expression $$(\tan1^{0} \tan2^{0} \tan 3^{0}...\tan89^{0})$$ is equal to

If $$b > 1, \sin t > 0, \cos t > 0$$ and $$\displaystyle \log_b(\sin t) = x$$, then $$\displaystyle \log_b(\cos t)$$ is equal to

If $$\cos9 \alpha= \sin \alpha$$ and $$9 \alpha < 90^{0}$$, then the value of $$\tan5 \alpha$$ is

In a right angle triangle $$\triangle ABC,\,\sin ^{ 2 }{ A } +\sin ^{ 2 }{ B } +\sin ^{ 2 }{ C } $$ is