Tangent subtraction and addition tan &#x2061;<!-- ⁡ --> 18 &#x2218;<!-- ∘ -->

Geovanni Holder

Geovanni Holder

Answered question

2022-06-03

Tangent subtraction and addition
tan 18 cot 36 + tan 72 cot 54 = ?

Answer & Explanation

Halle Mckee

Halle Mckee

Beginner2022-06-04Added 4 answers

Hint: Let tan 18 = t. Then you need
t 2 t 1 t 2 + 1 t 1 t 2 2 t = 1 2 t 2 3 t 4 2 t ( 1 t 2 )
To find t, you may want to use 36 = 90 54
tan ( 2 18 ) = cot ( 3 18 ) 2 t 1 t 2 = 1 3 t 2 3 t t 3
Solve the biquadratic and select the right root!

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