Question

The general solution of cot⁡θ+tan⁡θ=2

• A. (A) θ=nπ2+(−1)nπ8
• B. (B) θ=nπ2+(−1)nπ4
• C. (C) θ=nπ2+(−1)nπ6
• D. (D) θ=nπ+(−1)nπ8

Answer 1

Answer: (B)

(B) θ=nπ2+(−1)nπ4

Answer 2

Given: cot⁡θ+tan⁡θ=2
⇒cos⁡θsin⁡θ+sin⁡θcos⁡θ=2,
use basic trigonometric identities
⇒sin2⁡θ+cos2⁡θsin⁡θcos⁡θ=2⇒1sin⁡θcos⁡θ=2,
Pythagorean identity⇒2sin⁡θcos⁡θ=1⇒sin⁡2θ=1,
double angle formula⇒sin⁡2θ=sin⁡π2
Hence general solution is given by,
2θ=nπ+(−1)nπ2, where n∈Z∴θ=nπ2+(−1)nπ4
Note that: If sin⁡θ=sin⁡α,
then general solution is given by
θ=nπ+(−1)nα
Hence, the correct option is (B).