Question

if 5sin theta =3,then sec theta +tan theta / sec theta-tan theta is equal to?
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Answer 1

Answer:

$\frac{sec\beta+tan\beta}{sec\beta-tan\beta}$ = 4

Step-by-step explanation:

Given: 5sinβ = 3 ⇒ sinβ = 3/5

Now, $\frac{sec\beta+tan\beta}{sec\beta-tan\beta}$ = $\frac{\frac{1}{cos\beta}+\frac{sin\beta}{cos\beta}}{\frac{1}{cos\beta}-\frac{sin\beta}{cos\beta}}$

⇒ $\frac{sec\beta+tan\beta}{sec\beta-tan\beta}$ = $\frac{1+sin\beta}{1-sin\beta}$

⇒ $\frac{sec\beta+tan\beta}{sec\beta-tan\beta}$ = $\frac{1+\frac{3}{5}}{1-\frac{3}{5}}$

⇒ $\frac{sec\beta+tan\beta}{sec\beta-tan\beta}$ = $\frac{\frac{5+3}{5}}{\frac{5-3}{5}}$

⇒ $\frac{sec\beta+tan\beta}{sec\beta-tan\beta}$ = $\frac{8}{2}$

⇒ $\frac{sec\beta+tan\beta}{sec\beta-tan\beta}$ = 4

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