Introduction to...

If $$a=\cos\alpha \cos\beta+\sin \alpha \sin\beta \cos\gamma$$
$$b=\cos\alpha \sin \beta-\sin\alpha \cos\beta \cos\gamma$$
and $$c=\sin \alpha \sin\gamma$$, then $$a^2+b^2+c^2$$ is equal to

The value of expression $$\displaystyle \frac{\sin 30^{\circ}+\tan 45^{\circ}-\sec 60^{\circ}}{\text{cosec}30^{\circ}-\cot 45^{\circ}-\cos 60^{\circ}}$$ = 

$$\text{cosec}^2 A \cot^2A-\sec^2A \tan^2A-(\cot^2A-\tan^2A)(\sec^2A+\text{cosec}^2A-1)$$ is equal to

If $$x=\dfrac {\sin^3p}{\cos^2p}, y=\dfrac {\cos^3p}{\sin^2p}$$ and $$\sin p + \cos p= \dfrac 12$$, then $$x+y$$ is equal to

Find the relation obtained by eliminating $$\displaystyle \theta $$ from the equation $$\displaystyle x=a\cos \theta +b\sin \theta  $$ and $$\displaystyle y=a\sin \theta -b\cos \theta $$

Which one of the following when simplified is not equal to one?

If $$\tan { \theta  } =\cfrac { p }{ q } $$, then what is $$\cfrac { p\sec { \theta  } -qco\sec { \theta  }  }{ p\sec { \theta  } +qco\sec { \theta  }  } $$ equal to?

If $$\frac{1 - cos x}{cos x (1 + cos x)} = \frac{sin \alpha}{cos x} - \frac{2}{1 + cos x}$$, then $$\alpha$$ =

If $$\cos P=\dfrac{1}{7}$$ and $$\cos Q=\dfrac{13}{14}$$, P and Q both are acute angle then the value of $$P-Q$$ will be?

In the figure given
$$\angle ABD=\angle PQD=\angle CDQ=\cfrac { \pi  }{ 2 } $$. If $$AB=x.PQ=z$$ and $$CD=y$$, then which one of the following is correct?