Given that sin 60 degree squareroot 32 use trigonometric id

Given that sin 60 degree = squareroot 3/2, use trigonometric identities to find the exact value of each of the following: Cos 30 degree cos^2 60 degree sec(pi/6) csc (pi/3) Given that cot theta = 2, use trigonometric identities to find the exact value of each of the following: Tan theta csc^2 theta tan (pi/2 - theta) sec^2 theta

Solution

1)   Given sin60 = 3/2

a) cos30 = cos(90-60) = sin60 = 3/2

b) cos^2 60 = 1 – sin^260 = 1 – ¾ = ¼

c) sec(pi/6) = sec(30) = 1/cos30 = 2/3

d) csc(pi/3) = csc60 = 1/sin60 = 2/3

2) Given cot = 2

a) tan = 1/cot = ½

b) csc² = 1 + cot² = 1 + 4 = 5

c) tan(pi/2 - ) = cot = 2

d) sec² = 1 + tan² = 1 + ¼ = 5/4