Mathematics

Question

What is the value of (tan 65° - tan 35°) / 1 + tan 65°tan 35°?
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  • Answer:

    [tex] \frac{ \sqrt{3} }{3} [/tex]

    Step-by-step explanation:

    We know that tangent angle addition formula is

    [tex] \tan(a - b) = \frac{ \tan(a) - \tan(b) }{1 + \tan(a) \tan(b) } [/tex]

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

    [tex] \tan(65 - 35) = \tan(30) [/tex]

    W e know that tan 30 is

    [tex] \tan(30) = \frac{ \sin(30) }{ \cos(30) } = \frac{ \frac{1}{2} }{ \frac{ \sqrt{3} }{2} } = \frac{1}{ \sqrt{3} } = \frac{ \sqrt{3} }{3} [/tex]