Question

Without using tables, evaluate the following: sin²30° cos²45° + 4tan²30° + sin²90° + cos²0°

Answer 1

sin²30° cos²45° + 4tan²30° + sin²90° + cos²0°

sin30° = `(1)/(2)`

cos45° = `(1)/sqrt(2)`

tan30° = `(1)/sqrt(3)`

sin90° = 1
cos0° = 1
sin²30° cos²45° + 4tan²30° + sin²90° + cos²0°

= `(1/2)^2 (1/sqrt(2))^2 + 4(1/sqrt(3))^2 + 1 + 1`

= `(1)/(4) xx (1)/(2) + (4)/(3) + 2`

= `(1)/(8) + (4)/(3) + 2`

= `(3 + 32 + 48)/(24)`

= `(83)/(24)`.