Question

Evaluate without using a trigonometric table:

cos 44° cosec 46° + tan 30° tan 60° − `sqrt2` cos 45° + tan² 60°

Answer 1

Given:

cos 44° cosec 46° + tan 30° tan 60° − `sqrt2` cos 45° + tan² 60°

Step 1:

cosec 46° = `1/sin 46° = 1/cos 44°`

cos 44° ⋅ cosec 46° = cos 44° ⋅ `1/(cos 44°) = 1`

Step 2:

tan 30° ⋅ tan 60° = `1/(sqrt3) ​⋅ sqrt3 = 1`

Step 3: 

cos 45° = `sqrt2/2`

`− sqrt2 ​⋅ cos 45° = − sqrt2​⋅ sqrt2/2 = − 1`

Step 4:

tan 60° = `sqrt3,`

`tan^2 60°  = (sqrt3)^2 = 3`

Step 5:

= 1 + 1 − 1 + 3   ...[add them all]

= 4