Question

निम्न का मान ज्ञात करें :

$$\frac{\tan ^{2} 60^{\circ}+4 \sin ^{2} 45^{\circ}+3 \sec ^{2} 30^{\circ}+5 \cos ^{2} 90^{\circ}}{\operatorname{cosec} 30^{\circ}+\sec 60^{\circ}-\cot ^{2} 30^{\circ}} .$$

Answer 1

Solution : मान $=\frac{(\sqrt{3})^{2}+4 \times\left(\frac{1}{\sqrt{2}}\right)^{2}+3 \times\left(\frac{2}{\sqrt{3}}\right)^{2}+5 \times 0}{2+2-(\sqrt{3})^{2}}$

$=\frac{3+4 \times \frac{1}{2}+3 \times \frac{4}{3}}{2+2-3}=\frac{3+2+4}{1}=9$