Question

prove that 2 sin ^ 2(π/6) + cosec^2 (7π/6) x cos ^2 (π/3) = 3/2.

Answer 1

Answer:

sin pi/6 = .5    sin^2 pi/6 = .25

cosec 7pi/6 = 1 / sin 7pi/6 = -1 /.5 so cosec^2 7pi/6 = 1/.25

cos pi/3 = .5     cos^2 pi/3 = .25

Then 2 * .25 + ((1 / .25) * .25) = .5 + 1 = 1.5

Answer 2

Answer:

Step-by-step explanation:

2sin²(π/6) + cosec²(7π/6).cos²(π/3) = 3/2

LHS = 2sin²(π/6) + cosec²(π+π/6).cos²(π/3)  

=2sin²(30°) +{-cosec(π/6)}.cos²(30°)

=2(1/2)² +cosec²(30°).cos²(30°)

= 2 × 1/4 + 4 × 1/4

= 1/2 + 1 = 3/2 = RHS