Introduction to...

If $$a\sin^{3}x+b\cos^{3}x=\sin x\cos x$$ and $$a\sin x=b\cos x$$ . If $$a,b,\sin x$$ and $$\cos x $$ all are non zero real numbers, then $$a^{2}+b^{2}=$$

If $$m\cos^{2}A+n\sin^{2}A=p,$$ then $$\cot^{2}A=$$

Match the following columns with the values obtained for the solution.

If $$\sin\theta+\cos\theta=a$$, then $$\sin^{4}\theta+\cos^{4}\theta=$$

If $$\displaystyle \sec\alpha=5x+\frac{1}{20x} $$, then $$\sec\alpha+\tan\alpha$$ is equal to

 If  $$k=(\sec A+\tan A)(\sec B+\tan B)(\sec C+\tan C)$$( $$\sec A$$$$-\tan A$$) ( $$\sec B$$$$-\tan B$$) ( $$\sec C$$$$-\tan C$$), then $$k$$ is equal to

If $$\tan { \theta  } +\sin { \theta  } =m, \tan { \theta - \sin { \theta =n }  } $$, then $$(m^{2}-n^{2})^{2}=$$.

If $$\cos x + \sec x = - 2$$ for a positive odd integer $$n$$ then $$\cos^nx + \sec^nx$$ is

In the given figure, $$ \triangle  ABC$$ is right angled at B and $$\cot A = \dfrac{3}{4}$$ . If $$AC =10$$cm, then the length of $$AB$$ is:

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