Introduction to...

If $$ \displaystyle \cos^2 \theta + sec^2 \theta = p$$, then

Given that $$ sin \, \alpha = \dfrac{1}{2} , cos \, \beta = \dfrac{1}{2} $$ , then value of $$ ( \alpha + \beta) $$ is 

$$2 \tan 45^{\circ} + \cos 45^{\circ} - \sin 45 ^{\circ} =? $$

Choose the correct alternative answer for the following question.
$$cosec \ 45^\circ= ?$$

If $$\theta =30^o$$, then $$\dfrac{1-\sin^22\theta}{\cos 2\theta}$$ is

If $$ \sqrt{3} \cos A = \sin A $$, then the value of $$ \cot A $$ is:

$$a \sec \theta+b\tan\theta=1, a^{2}\sec^{2}\theta-b^{2}\tan^{2}\theta=5$$
Then $$ a^{2}(b^{2}+4)=$$

If $$a \sin^{2}x+b\cos^{2}x=c, b\sin^{2}y+a\cos^{2}y=d$$ and $$a \tan x=b\tan y,$$ then $$\displaystyle \frac{a^{2}}{b^{2}}$$ equals to

$$\cot^{2}\alpha=1+\mathrm{a}^{2}$$ then $$\text{cosec}\,\alpha+\cot^{3}\alpha\sec\alpha=$$?

$$\displaystyle {x}=\frac{\sin^{3}{p}}{\cos^{2}{p}}, \displaystyle {y}=\frac{\cos^{3}{p}}{\sin^{2}{p}}$$ and $$\sin p$$ $$+$$ $$\cos p $$ $$= \dfrac 12$$ then $${x}+{y}=$$