The value of 2 tan-10-3 -10-4 cos-10 is

The correct option is B 0 We have, 2 tan π/10+3 sec π/10 4 cos π/10 =2 tan 18^∘ + 3 sec 18^∘ 4 cos 18^∘ =2 sin 18^∘/cos 18^∘+ 3 ×1/cos 18^∘ 4 cos 18^∘ = 2 × ...

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Byju's Answer

Standard XII

Mathematics

Trigonometric Ratios for Sum of Two Angles

The value of ...

Question

The value of $2 t a n \frac{π}{10} + 3 s e c \frac{π}{10} - 4 c o s \frac{π}{10}$ is

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$\sqrt{5}$

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none of these

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Solution

The correct option is A
0

We have,

$2 t a n \frac{π}{10} + 3 s e c \frac{π}{10} - 4 c o s \frac{π}{10} = 2 t a n 18^{\circ} + 3 s e c 18^{\circ} - 4 c o s 18^{\circ} = 2 \frac{s i n 18^{\circ}}{c o s 18^{\circ}} + 3 \times \frac{1}{c o s 18^{\circ}} - 4 c o s 18^{\circ}$

$= 2 \times \frac{\frac{\sqrt{5} - 1}{4}}{\frac{\sqrt{10 + 2 \sqrt{5}}}{4}} + 3 \times \frac{1}{\frac{\sqrt{10 + 2 \sqrt{5}}}{4}} - 4 \times \frac{\sqrt{10 + 2 \sqrt{5}}}{4} = 2 \times \frac{\sqrt{5} - 1}{\sqrt{10 + 2 \sqrt{5}}} + 3 \times \frac{4}{\sqrt{10 + 2 \sqrt{5}}} - \sqrt{10 + 2 \sqrt{5}} = \frac{2 \sqrt{5} - 2 + 12 - (\sqrt{10 + 2 \sqrt{5}})^{2}}{(\sqrt{10 + 2 \sqrt{5}})} = \frac{2 \sqrt{5} + 10 - 10 - 2 \sqrt{5}}{(\sqrt{10 + 2 \sqrt{5}})} = 0$

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The value of 2 tan π10+3 sec π10−4 cos π10 is

The value of $2 t a n \frac{π}{10} + 3 s e c \frac{π}{10} - 4 c o s \frac{π}{10}$ is