Question

Find the value of the $\frac{sin{17}^{\circ }sec{73}^{\circ }-cose{c}^2{67}^{\circ }}{se{c}^2{45}^{\circ }-tan{23}^{\circ }tan{67}^{\circ }+co{t}^2{67}^{\circ }}$

• A. $co{s}^2{67}^{\circ }$
• B. $-co{s}^2{67}^{\circ }$
• C. $co{s}^2{73}^{\circ }$
• D. $-co{s}^2{73}^{\circ }$

Answer 1

The correct option is B $-co{s}^2{67}^{\circ }$

$\frac{sin{17}^{\circ }sec{73}^{\circ }-cose{c}^2{67}^{\circ }}{se{c}^2{45}^{\circ }-tan{23}^{\circ }tan{67}^{\circ }+co{t}^2{67}^{\circ }}$

$\frac{sin{17}^{\circ }sec({90}^{\circ }-{17}^{\circ })-cose{c}^2{67}^{\circ }}{se{c}^2{45}^{\circ }-tan{23}^{\circ }tan({90}^{\circ }-{23}^{\circ })+co{t}^2{67}^{\circ }}$ $\left[sec\right(90-\theta )=cosec\theta ,tan(90-\theta )=cot\theta ]$

$\frac{sin{17}^{\circ }cosec{17}^{\circ }-cose{c}^2{67}^{\circ }}{se{c}^2{45}^{\circ }-tan{23}^{\circ }cot{23}^{\circ }+co{t}^2{67}^{\circ }}$
$[sin\theta cosc\theta =1,tan\theta cot\theta =1]$

$\frac{1-cose{c}^2{67}^{\circ }}{2-1+co{t}^2{67}^{\circ }}$

$\frac{1-cose{c}^2{67}^{\circ }}{1+co{t}^2{67}^{\circ }}[cose{c}^2\theta =1+co{t}^2\theta ]$

$\frac{-co{t}^2{67}^{\circ }}{cose{c}^2{67}^{\circ }}$

$\frac{\frac{-co{s}^2{67}^{\circ }}{si{n}^2{67}^{\circ }}}{\frac{1}{si{n}^2{67}^{\circ }}}$
$[cot\theta =\frac{cos\theta }{sin\theta },cosec\theta =\frac{1}{sin\theta }]$

$-co{s}^2{67}^{\circ }$