Write the word or phrase that best completes each statement

Write the word or phrase that best completes each statement or answers the question. Verify that the equation is an identity. cot^2 u/2 = csc u + cot u/csc u - cot u Choose the one alternative that best completes the statement or answers the question. Solve the problem. Use the exact value cos 36 degree = squareroot 5 + 1/4 and identities to find the exact value of csc 36 degree. squareroot 5 + 1 B) (squareroot 10 + 2 squareroot 5)(10 - 2 squareroot 5)/10 squareroot 10 - 2 Squreroot 5/2 D) (squareroot 10 - 2 squareroot 5)(10 + 2 squareroot 5)/20

Solution

cos36 = [sqrt(5) +1]/4

csc36 = 1/ sin36

sin36 = sqrt[( 1 - cos^2(36))]

= sqrt[ 1 - (1 +5 +2sqrt5)/16 ]

= sqrt[(10 -2sqrt5)/16]

= sqrt(10 -2sqrt5]/4

csc36 = 4/sqrt(10 -2sqrt5]

rationalise the denominator:

= 4sqrt(10 + 2sqrt5]/(sqrt(100 - 20) )

= 4sqrt(10 +2sqrt5]/sqrt(80)