sec⁡θ=a2+b2a2−b2, where a,b,∈R, gives real values of θ if and only if

Clearly,

$a^{2} + b^{2} \geq a^{2} - b^{2}$ for all $| | a | \neq | b ∣\neq 0$ ,

$\Rightarrow \frac{a^{2} + b^{2}}{a^{2} - b^{2}} \geq 1$ or. $\frac{a^{2} + b^{2}}{a^{2} - b^{2}} \leq - 1$

$∴ \sec θ = \frac{a^{2} + b^{2}}{a^{2} - b^{2}}$ is meaningful.

Thus, $\sec θ = \frac{a^{2} + b^{2}}{a^{2} - b^{2}}$ gives real values of $θ$ if and only $| a | \neq | b | \neq 0$

$\sec θ = \frac{a^{2} + b^{2}}{a^{2} - b^{2}}$ , where $a, b, \in R$ , gives real values of $θ$ if and only if