Question

Using a double angle formula how would you find the exact value of this expression?


Cos²105° - sin²105°

Answer 1

cos^2(105) - sin^2(105)
= cos 2(105)
= cos 210
= cos (180 + 30)
= cos180cos30 - sin30sin180
= -1(√3/2) - (1/2)(0)
= -√3/2

Answer 2

Hey thanks can you point me in the direction to solving this problem

2tan(5pi/12)/1-tan²(5pi/12)

Answer 3

Did you recoginize that your expression matches the formula for tan 2A ?

tan 2A = 2tanA/(1-tan^2 A)
so
2tan(5pi/12)/1-tan²(5pi/12)
= tan(5pi/6) or tan 150º

tan 150
= -tan 30 or - tan(pi/6)
= -1/√3