Question

If secx + tanx = 3, find cosecx + cotx.
1. 3
2. 1
3. 0
4. 2

Answer 1

Correct Answer - Option 4 : 2

Given:

secx + tanx = 3

Concept Used:

If secx + tanx = y. then secx - tanx = 1/y

cosec²x - cot²x = 1

tanx = 1/cotx

Calculation:

secx + tanx = 3      ----(i)

secx - tanx = 1/3      ----(ii)

Subtracting (ii) from (i), we get 2tanx,

2tanx = 8/3

⇒ tanx = 4/3

⇒ cotx = 3/4

cosecx = √(1 + cot²x)

⇒ √(1 + 9/16)

⇒ √(25/16)

⇒ 5/4

cosecx + cotx = 5/4 +3/4 

⇒ 2

∴ The value of cosecx + cotx is 2.