TRIG help, #2?

Question

this is the last one, i promise!

i need to find the value of 15degrees tan

when sin(a)+cos(b) x sin(b)+cos(a)

i mean using sin(a)+cos(b) x sin(b)+cos(a)

Answer 1

You're looking for the exact value of

tan 15°

right?

Then I'd suggest using either of the half-angle formulas for tangent:

tan θ/2 = sin θ/(1 + cos θ)

or

tan θ/2 = (1 - cos θ)/sin θ

Either way, 15° = 30°/2, and cos 30° = √3/2 and sin 30° = 1/2, so:

tan 30°/2 = tan 15° = (1 - √3/2) / (1/2) = (1 - √3/2) x (2/1) = 2 - √3