Question

Without using a calculator, find the exact value of the expression: 8cos^2 (45)+30csc^2 (45).

Answer 1

64

Explanation:

using the identity

csc x =
`(1)/(sinx)`

and the exact values

sin45° = cos45° =
`(1)/(√(2) )`

8cos²45° + 30csc² 45°

= 8 (
`(1)/(√(2) )` )² + 30 (
`(1)/(sin^245)` )

= 8 (
`(1)/(2)` ) + 30 (
`(1)/(((1)/(√(2))^2 ) )` )

= 4 + 30 (
`(1)/((1)/(2) )` )

= 4 + 30 (2)

= 4 + 60

= 64