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(a / 4 – b / 2 + 1)2 expand it with suitable identites.

The given expression is \(\begin{array}{l}\left(\frac{a}{4}-\frac{b}{2}+1\right)^{2}\\ \text { The suitable identity is }(x+y+z)^{2}=x^{2}+y^{2}+z^{2}+2 x y+2 y z+2 x z\\ \left(\frac{a}{4}-\frac{b}{2}+1\right)^{2}\\ =\left(\frac{a}{4}\right)^{2}+2\left(-\frac{b}{2}\right)^{2}+(1)^{2}+2\left(\frac{a}{4}\right)\left(-\frac{b}{2}\right)+2\left(-\frac{b}{2}\right)(1)+2\left(\frac{a}{4}\right)(1)\\... View Article

Evaluate cos 45 / (sec 30 + cosec 30).

The given expression is \(\begin{array}{l}\left(\cos 45^{\circ}\right) /\left(\sec 30^{\circ}+{cosec} 30^{\circ}\right) \\ =\frac{\frac{1}{\sqrt{2}}}{\frac{2}{\sqrt{3}}+2}=\frac{\frac{1}{\sqrt{2}}}{\frac{2+2 \sqrt{3}}{\sqrt{3}}} \\ =\frac{\sqrt{3}}{\sqrt{2}(2+2 \sqrt{3})}=\frac{\sqrt{3}}{2 \sqrt{2}+2 \sqrt{6}} \\ =\frac{\sqrt{3}(2 \sqrt{6}-2... View Article