Question

6 tan 30°cot 60°+ 3 tan 60°cot 30°+ tan 20°cot 20° tan 45°

Answer 1

Answer:

answer is 13

Step-by-step explanation:

Answer 2

Answer:

Required value of the given term is 12.

Step-by-step explanation:

Given,

6 tan 30°cot 60°+ 3 tan 60°cot 30°+ tan 20°cot 20° tan 45°

$= 6 \times \frac{1}{ \sqrt{3} } \times \frac{1}{ \sqrt{3} } + 3 \times \sqrt{3} \times \sqrt{3} + tan {20}^{o} \times \frac{1}{tan {20}^{o} } \times 1$

$= 6 \times \frac{1}{ \sqrt{3} \times \sqrt{3} } + 3 \times 3 + 1 \times 1 \\ = 6 \times \frac{1}{3} + 9 + 1 \\ = 2 + 9 + 1 \\ = 12$

Here applied formula,

$tan {30}^{o} = \frac{1}{ \sqrt{3} } \\ tan {45}^{o} = 1 \\ tan {60}^{o} = \sqrt{3} \\ cot {30}^{o} = \sqrt{3} \\ cot {60}^{o} = \frac{1}{ \sqrt{3} } \\ cotx = \frac{1}{tanx}$

Some important Trigonometry formula,

$sin(x) = \cos(\frac{\pi}{2} - x) \\ \tan(x) = \cot(\frac{\pi}{2} - x) \\ \sec(x) = \csc(\frac{\pi}{2} - x) \\ \cos(x) = \sin(\frac{\pi}{2} - x) \\ \cot(x) = \tan(\frac{\pi}{2} - x) \\ \csc(x) = \sec(\frac{\pi}{2} - x)$

know more about Trigonometry,

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