Question

if tan40+2tan10=cotA then A=

Answer 1

Answer on Question #49552 – Math – Trigonometry

if $\tan 40 + 2\tan 10 = \cot A$ then $A =$

Solution

$$\tan 40{}^\circ + 2\tan 10{}^\circ = \cot A$$

Using calculator:

$$\cot A = \tan 40{}^\circ + 2\tan 10{}^\circ = \tan \left(\frac{2\pi}{9}\right) + 2\tan \left(\frac{\pi}{18}\right) = 1.192.$$

Using inverse trigonometric function, obtain

$$A = \operatorname{arccot}(1.192) = 40{}^\circ$$

Answer: $A = 40{}^\circ$.

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