Question

Evalute : $\frac{sec{29}^{\circ }}{cosec{61}^{\circ }}$ + 2 cot $8^{\circ }$ cot ${17}^{\circ }$ cot${45}^{\circ }$ cot${73}^{\circ }$ cot${82}^{\circ }$.

Answer 1

$\frac{sec{29}^{\circ }}{cosec{61}^{\circ }}$ + 2 cot $8^{\circ }$ cot ${17}^{\circ }$ cot${45}^{\circ }$ cot${73}^{\circ }$ cot${82}^{\circ }$

= $\frac{sec{29}^{\circ }}{cosec({90}^{\circ }-{29}^{\circ })}$ + 2 cot $8^{\circ }$ cot ${17}^{\circ }$ (1) cot (${90}^{\circ }-{17}^{\circ })$ cot (${90}^{\circ }-8^{\circ })$

= $\frac{sec{29}^{\circ }}{sec{29}^{\circ }}$ + 2cot $8^{\circ }$ cot ${17}^{\circ }$ tan ${17}^{\circ }$ tan $8^{\circ }$ ($\because cot({90}^{\circ }-\theta$)=tan$\theta$

= 1 + 2 cot $8^{\circ }$ cot ${17}^{\circ }$ $\frac{1}{cot{17}^{\circ }}$ . $\frac{1}{cot{8}^{\circ }}$ .......... $(\because tan\theta =\frac{1}{cot\theta }$)

= 1+2

=3