Problem: The minimum value of sin2A−3cos2A is attained when A is
Answer Choices:
A. −180∘
B. 60∘
C. 120∘
D. 0∘
E. none of these
Solution:
Writing
sin2A−3cos2A=2[21sin2A−23cos2A]=2sin(2A−60∘)=2[cos60∘sin2A−sin60∘cos2A]
we see that the last expression is minimum when sin(2A−60∘)−−1 or when
2A−60∘=270∘+(360 m)∘,m=0,±1,±2,⋯
Solving for A we get a minimum when
A=660∘+(720 m)2,m=0,±1,±2,⋯.
None of (A) through (D) satisfy this equation.