Introduction to...

Refer to the above figure and find the length of $$AC$$, if the area of triangle $$ABC$$ is $$15$$.

Calculate the value of $$x$$ if the value of $$\theta = 67^{\circ}$$ in the right angled triangle shown in the above figure.

Find the value of $$\tan (3x) \cot (3x) $$ if it is defined.

The length of side $$DF$$, if the area of triangle $$DEF$$ is $$32\sqrt {3}$$ square units is

Simplify $$12\sqrt{3}-(8 \cos x)\left(\displaystyle\frac{3\sqrt 3}{2}\cos x\right)$$.

Simplify $$1 - 2\sin^{2}\theta - 2\cos^{2} \theta $$.

Find the length of $$AC$$ in the above figure.

In the figure, $$ABCD$$ is a rectangle. Calculate the area of $$ABCD$$.

If $$t = 45^{\circ}$$, what is $$\sec (t) \sin (t) - \mathrm{cosec} (t) \cos (t)$$?

Find the value of $$\dfrac {\cos 75^{\circ} . \sin 12^{\circ}. \cos 18^{\circ}}{\sin 15^{\circ}. \cos 78^{\circ} . \sin 72^{\circ}}$$