Question

Find the value of the following without using a table:

sin² 30° + cos² 60° + cosec 30°

Answer 1

Given:

sin² 30^∘ + cos² 60° + csc 30°

Step 1:

sin 30^∘ = `1/2 → sin^2 30° = 1/4`

cos 60°  = `1/2 → cos^2 60° = 1/4`

cosec 30° = `1/(sin 30°) = 1/ (1/2) = 2`

Step 2: 

sin² 30^∘ + cos² 60^∘ + csc 30^∘ = `1/4 + 1/4 + 2 = 1/2 + 2 = 5/2`

sin² 30° + cos² 60° + cosec 30° = `5/2 = 2.5`

= 2.5 or `2 1/2`