Value of 3- 80- 20- 80- 20- is equal to

The correct option is C 3 + cos 80^∘cos 20^∘/sin 80^∘sin 20^∘/cos 80^∘/sin 80^∘ + cos 20^∘/sin 20^∘ = 2sin 80^∘sin 20^∘ + cos 80^∘cos 20^∘ + sin 80^∘sin 20^∘/s ...

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Byju's Answer

Standard XII

Mathematics

Sign of Trigonometric Ratios in Different Quadrants

Value of 3+ 8...

Question

Value of $\frac{3 + cot 80^{\circ} cot 20^{\circ}}{cot 80^{\circ} + cot 20^{\circ}}$ is equal to

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Solution

The correct option is B
$\frac{3 + \frac{cos 80^{\circ} cos 20^{\circ}}{sin 80^{\circ} sin 20^{\circ}}}{\frac{cos 80^{\circ}}{sin 80^{\circ}} + \frac{cos 20^{\circ}}{sin 20^{\circ}}} = \frac{2 sin 80^{\circ} sin 20^{\circ} + cos 80^{\circ} cos 20^{\circ} + sin 80^{\circ} sin 20^{\circ}}{sin 20^{\circ} cos 80^{\circ} + cos 20^{\circ} sin 80^{\circ}}$
$= \frac{cos 60^{\circ} - cos 100^{\circ} + cos 60^{\circ}}{sin 100^{\circ}} = \frac{1 - cos 100^{\circ}}{sin 100} = tan 50^{\circ}$

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Value of 3+cot80∘cot20∘cot80∘+cot20∘ is equal to

The correct option is B 3+cos80∘cos20∘sin80∘sin20∘cos80∘sin80∘+cos20∘sin20∘=2sin80∘sin20∘+cos80∘cos20∘+sin80∘sin20∘sin20∘cos80∘+cos20∘sin80∘ =cos60∘−cos100∘+cos60∘sin100∘=1−cos100∘sin100=tan50∘

Value of $\frac{3 + cot 80^{\circ} cot 20^{\circ}}{cot 80^{\circ} + cot 20^{\circ}}$ is equal to