Introduction to...

If $$x= \sec\phi - \tan\phi $$ and  $$y= cosec \phi  $$ then:

The value of $$\tan 5^{\circ}\tan 10^{\circ}\tan 15^{\circ}\cdots \tan 85^{\circ}$$ is

If $$\displaystyle\tan \alpha +\cot \alpha =p$$, then find $$\displaystyle\tan^{2} \alpha +\cot^{2} \alpha $$     

$$\cos ^{2} 60^{\circ}+\sin ^{2} 30^{\circ} = \displaystyle \frac{1}{a}$$
Then $$a=$$

If $$\displaystyle \tan \theta =a-\frac{1}{4a}$$, then $$\sec \theta -\tan \theta $$ equals

The expression $$\displaystyle f\left ( \theta \right )= \frac{1}{\tan \theta+\sec \theta+\cot \theta+\text{cosec} \theta}$$ is equivalent to

$$\sin 60^{0} \: \cos 30^{0}+\cos 60^{0} \: \sin 30^{0}= 1$$

$$ABC$$ is an isosceles right-angled triangle. Assuming $$AB= BC= x$$, find the value of each of the following trigonometric ratios:

The value of $$\displaystyle \frac{\cos 3A-2\cos 4A}{\sin 3A+2\sin 4A}$$ is $$\displaystyle \frac{1-\sqrt{2}}{1+\sqrt{6}}$$, when $$A= 15^{0}$$.

If $$\tan \angle ADC= 1$$ and $$\sin \angle ABC=4:5$$, then measure of $$CD$$ is: