Find the value of:
$\sin 75^{\circ}$
$\sin 75^{\circ}=\sin \left(45^{\circ}+30^{\circ}\right)$
$=\sin 45^{\circ} \cos 30^{\circ}+\cos 45^{\circ} \sin 30^{\circ}$
$[\sin (x+y)=\sin x \cos y+\cos x \sin y]$
$=\left(\frac{1}{\sqrt{2}}\right)\left(\frac{\sqrt{3}}{2}\right)+\left(\frac{1}{\sqrt{2}}\right)\left(\frac{1}{2}\right)$
$=\frac{\sqrt{3}}{2 \sqrt{2}}+\frac{1}{2 \sqrt{2}}=\frac{\sqrt{3}+1}{2 \sqrt{2}}$
Which of the following relations is correct
If $(\sec \alpha + \tan \alpha )(\sec \beta + \tan \beta )(\sec \gamma + \tan \gamma )$$ = \tan \alpha \tan \beta \tan \gamma $, then $(\sec \alpha - \tan \alpha )(\sec \beta - \tan \beta )$$(\sec \gamma - \tan \gamma ) = $
If $\sin \theta + \cos \theta = m$ and $\sec \theta + {\rm{cosec}}\theta = n$, then $n(m + 1)(m - 1) = $
If $\cot x=-\frac{5}{12}, x$ lies in second quadrant, find the values of other five trigonometric functions.
$(m + 2)\sin \theta + (2m - 1)\cos \theta = 2m + 1,$ if