Question

Find the indicated value. Use either half angle formulas or sum and difference formulas.

Sin15° =

Tan75° =

Answer 1

By the angle difference formula for sines, we have:


`\sin 15^\circ = \sin 45^\circ \cos 30^\circ - \sin 30^\circ \cos 45^\circ = \frac{sqrt{6}}{4} - \frac{sqrt{2}}{4} = (√(6) - √(2))/(4).`

By the angle sum formula for tangents, we have:


`\tan 75^\circ = (\tan 45^\circ + \tan 30^\circ)/(1 - \tan 45^\circ \tan 30^\circ) = (1+(√(3))/(3))/(1 - (√(3))/(3)) = (3 + √(3))/(3 - √(3))`.

Rationalizing the denominator gives
`(12+6√(3))/(6) = 2+√(3)` as the final answer.