Problem: If θ is an acute angle and sin21θ=2xx−1, then tanθ equals
Answer Choices:
A. x
B. x1
C. x+1x−1
D. xx2−1
E. x2−1
Solution:
Using the formula for the cosine of twice an angle 21θ.
cosθ=cos221θ=1−2sin221θ=1−2(2xx−1)=x1
Since
secθ=cosθ1=x,tan2θ=sec2θ−1=x2−1 and tanθ=x2−1