Question

Evaluate :
2 sin 68°/cos 22 - 2 cot 15/tan 75 -3 tan 40 tan 45 tan 50
​

Answer 1

SOLUTION

TO DETERMINE

$\displaystyle \sf{ \frac{2 \sin {68}^{ \circ} }{ \cos {22}^{ \circ} } - \frac{2 \cot {15}^{ \circ} }{ \tan {75}^{ \circ} } - 3 \tan {40}^{ \circ} \tan {45}^{ \circ} \tan {50}^{ \circ} \: }$

EVALUATION

$\displaystyle \sf{ \frac{2 \sin {68}^{ \circ} }{ \cos {22}^{ \circ} } - \frac{2 \cot {15}^{ \circ} }{ \tan {75}^{ \circ} } - 3 \tan {40}^{ \circ} \tan {45}^{ \circ} \tan {50}^{ \circ} \: }$

$= \displaystyle \sf{ \frac{2 \sin {68}^{ \circ} }{ \cos ( {90}^{ \circ} - {68}^{ \circ}) } - \frac{2 \cot {15}^{ \circ} }{ \tan( {90}^{ \circ} - {15}^{ \circ}) } - 3 \tan {40}^{ \circ} \tan {45}^{ \circ} \tan ( {90}^{ \circ} - {40}^{ \circ}) }$

$= \displaystyle \sf{ \frac{2 \sin {68}^{ \circ} }{ \sin {68}^{ \circ} } - \frac{2 \cot {15}^{ \circ} }{ \cot {15}^{ \circ} } - 3 \tan {40}^{ \circ} \tan {45}^{ \circ} \cot {40}^{ \circ} \: }$

$= \displaystyle \sf{2 -2 - 3 \tan {40}^{ \circ} \times 1 \times \frac{1}{\tan {40}^{ \circ}} \: }$

$= \displaystyle \sf{2 -2 - 3 \: }$

$\sf{ = - 3}$

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