Question

What is the value of (tan 65° - tan 35°) / 1 + tan 65°tan 35°?
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0 V3/3

Answer 1

`( √(3) )/(3)`

Explanation:

We know that tangent angle addition formula is

`\tan(a - b) = ( \tan(a) - \tan(b) )/(1 + \tan(a) \tan(b) )`

This is in form already. Based on the value, a is 65 and b is 35 so let just subtract that

`\tan(65 - 35) = \tan(30)`

W e know that tan 30 is

`\tan(30) = ( \sin(30) )/( \cos(30) ) = ( (1)/(2) )/( ( √(3) )/(2) ) = (1)/( √(3) ) = ( √(3) )/(3)`