Question

1. The least value of 2 sin²0 + 3 cos20 is
(a) 1
(b) 2
(c) 3
(d) 0​

Answer 1

2Sin²∅+3cos2∅

=2sin²∅+3(cos²∅-sin²∅)

=2sin²∅+3cos²∅-3sin²∅

=3cos²∅-sin²∅

=3cos²∅-(1-cos²∅)

=3cos²∅-1+cos²∅

=4cos²∅-1

4cos²∅=1

cos²∅=1/4

cos∅=1/2

∅=60°