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Mathematics
25.04.2023 01:25
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Using addition formula solve tan 15

Using addition formula solve tan 15
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chefdnguyen
chefdnguyen
5,0(71 marks)

2 - \sqrt{3}

Step-by-step explanation:

Using the addition formula for tangent

tan(A - B) = \frac{tanA-tanB}{1+tanAtanB} and the exact values

tan45° = 1 , tan60° = \sqrt{3} , then

tan15° = tan(60 - 45)°

tan(60 - 45)°

= \frac{tan60-tan45}{1+tan60tan45}

= \frac{\sqrt{3}-1 }{1+\sqrt{3} }

Rationalise the denominator by multiplying numerator/ denominator by the conjugate of the denominator.

The conjugate of 1 + \sqrt{3} is 1 - \sqrt{3}

= \frac{(\sqrt{3}-1)(1-\sqrt{3}) }{(1+\sqrt{3})(1-\sqrt{3}) } ← expand numerator/denominator using FOIL

= \frac{\sqrt{3}-3-1+\sqrt{3} }{1-3}

= \frac{-4+2\sqrt{3} }{-2}

= \frac{-4}{-2} + \frac{2\sqrt{3} }{-2}

= 2 - \sqrt{3}

maylinox4330
maylinox4330
5,0(85 marks)

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Step-by-step explanation:

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