Question

One of the general values of θ satisfying the equation

tan²θ + sec 2θ = 1 is

• A. 2nπ
• B. nπ± $\frac { \pi } { 4 }$
• C. nπ± $\frac { \pi } { 3 }$
• D. None of these

Answer 1

Answer: (C)

nπ± $\frac { \pi } { 3 }$

Answer 2

The given equation can be written as

tan² θ + $\frac { 1 + \tan ^ { 2 } \theta } { 1 - \tan ^ { 2 } \theta } = 1$

⇒ tan² θ(tan² θ – 3) = 0 ⇒ tan θ = ± $\sqrt { 3 }$.