Question

if sin theta=12/13 find the value of
sec theta + tan theta/sec theta- tan theta

Answer 1

hope it is useful for u

Answer 2

Concept:

The trigonometric ratios are given by,
sin∅ = $\frac{Opposite Side}{Hypotenuse}$  Cos∅ = $\frac{Adjacent Side}{Hypotenuse}$

Given:

The value of sin∅ = $\frac{12}{13}$

Find:

We are asked to find the value of $\frac{sec\ \phi + \ tan \ \phi }{sec\ \phi - \ tan \ \phi}$ .

Solution:

$\frac{sec\ \phi + \ tan \ \phi }{sec\ \phi - \ tan \ \phi}$

= $\frac{\frac{1}{cos \ \phi} + \frac{sin \ \phi}{cos \ \phi}}{\frac{1}{cos \ \phi} - \frac{sin \ \phi}{cos \ \phi}}$

= $\frac{1 + sin \phi}{1 - sin \phi}$

= $\frac{1 + \frac{12}{13} }{1- \frac{12}{13}}$

= $\frac{13 + 12}{13 - 12}$

= 25

Thus , the value of the expression  $\frac{sec\ \phi + \ tan \ \phi }{sec\ \phi - \ tan \ \phi}$ is 25.

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