The absolute of the expression \frac{1+\sqrt 3 \tan 1^{\circ}}{\sqrt 3-\tan

Jett Castaneda

Jett Castaneda

Answered question

2022-01-26

The absolute of the expression 1+3tan13tan1tan89cot3 is equal to...

Answer & Explanation

Eleanor Shaffer

Eleanor Shaffer

Beginner2022-01-27Added 16 answers

You can prove that tan3xtanx=tan(60x)tan(60+x), so tan89cot3=tan3tan1=tan59tan61.
And 1+3tan13tan1=1+tan60tan1tan60tan1=1tan(601)=1tan59
Thus the expression equals tan61

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