Mathematics Problems and Solutions ( U . K . Z . M )

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ABC is a triangle having  BC = 2 AB . Bisect  BC  in  D  and  BD  in  E . Prove that  AD  bisects  $\displaystyle \angle \ CAE.$ Solution...

$\displaystyle A+B+C={{180}^{\circ }}$ $\displaystyle 3\sin A+4\cos B=6$ $\displaystyle 3\cos A+4\sin B=\sqrt{{13}}$ $\displaystyle \s...

$\displaystyle \text{Prove}\ \text{that}\ \ \ \frac{{\cos 8x-\cos 7x}}{{1+2\cos 5x}}=\cos 3x-\cos 2x\ .$ Solution $\displaystyle \ \ \ \...

In the diagram below , the lengths of the three sides of the triangle are $\displaystyle a\ cm\ ,\ b\ cm\ \text{and}\ c\ cm$ . It is given t...

Find the value of $\displaystyle (\ \text{i}\ )\ \ \ {{\sin }^{4}}\frac{\pi }{8}+{{\cos }^{4}}\frac{\pi }{8}+{{\sin }^{4}}\frac{{7\pi }}{8}...

Find the value of $\displaystyle (\ \text{i}\ )\ \ \ \ \frac{{\sin {{{80}}^{\circ }}}}{{\sin {{{20}}^{\circ }}}}-\frac{{\sqrt{3}}}{{2\sin {...