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

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

1. A

$a=b\ne 0$

2. B

$|a|\ne |b|\ne 0$

3. C

$a+b=0,a\ne 0$

4. D

none of these

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### Solution:

Clearly,

${a}^{2}+{b}^{2}\ge {a}^{2}-{b}^{2}$ for all $||a|\ne |b\mid \ne 0$,

or. $\frac{{a}^{2}+{b}^{2}}{{a}^{2}-{b}^{2}}\le -1$

is meaningful.

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

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