Question

Evaluate the following:

tan 30° cosec 60° + tan 60° sec 30°

Answer 1

Given: tan 30° · cosec 60° + tan 60° · sec 30°.

Step-wise calculation:

1. Use standard values:

`tan 30^circ = 1/sqrt(3)`

cosec 60° = `1/(sin 60^circ)` 

= `1/(sqrt(3)/2)`

= `2/sqrt(3)`

`tan 60^circ = sqrt(3)`

`sec 30^circ = 1/(cos 30^circ)`

= `1/(sqrt(3)/2)`

= `2/sqrt(3)`

2. Compute each product:

tan 30° · cosec 60° 

= `(1/sqrt(3)) · (2/sqrt(3))`

= `2/3`

tan 60° · sec 30° 

= `(sqrt(3)) · (2/sqrt(3))`

= 2

3. Add:

`2/3 + 2 = 2/3 + 6/3`

= `8/3`

tan 30° · cosec 60° + tan 60° · sec 30° = `8/3`