Question

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Use half angle to find the exact value of tan 15º

Answer 1

0.2679

Explanation:

Knowing that tg 45⁰ = 1, tg 30⁰=
`1/√(3)`, and tg (a-b) =
`(tg a - tg b)/(1+tg a. tg b)` we have: tg 15⁰ = tg (45⁰-30⁰) = (tg 45⁰-tg 30⁰) / (1+tg 45⁰. tg 30⁰) =
`(1-1/√(3) )/(1+1/√(3) ) = ((√(3)-1 )/(√(3) ) )/((√(3)+1 )/(√(3) ) ) = (√(3)-1 )/(√(3)+1 )` = 0.73205/2.73205 = 0.26794