# If tanθ + cotθ = 5, then

If tanθ + cotθ = 5, then tan^{2}θ + cot^{2}θ is:

- 25
- 26
- 23
- 24

**Answer: (3) 23**

**Explanation:-
**tanθ + cotθ = 5 ………………. (1)

Square on both side,

(tanθ + cotθ)

^{2}= 5

^{2}

tan

^{2}θ + cot

^{2}θ + 2 tanθ cotθ = 25

tan

^{2}θ + cot

^{2}θ + 2 cotθ/cotθ = 25 (tanθ = 1/cotθ)

tan

^{2}θ + cot

^{2}θ + 2 = 25

tan

^{2}θ + cot

^{2}θ = 25 – 2

tan

^{2}θ + cot

^{2}θ = 23

Then, the tanθ + cotθ = 5, then tan^{2}θ + cot^{2}θ is 23.

Hence, the answer is (3) 23.