Question

Sec Ф -tanФ/sec Ф + tan Ф=1/4 .find sin Ф
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Answer 1

Required Answer:-

Given:

• $\sf \frac{ \sec(x) - \tan(x) }{ \sec(x) + \tan(x) } = \frac{1}{4}$

To find:

• The value of $\sf \sin(x)$

Answer:

• The value of sin(x) is 3/5

Solution:

$\sf \frac{ \sec(x) - \tan(x) }{ \sec(x) + \tan(x) } = \frac{1}{4}$

$\sf \implies 4( \sec(x) - \tan(x) ) = \sec(x) + \tan(x)$

$\sf \implies 4\sec(x)-4\tan(x)-\sec(x) - \tan(x) = 0$

$\sf \implies 3\sec(x)-5\tan(x) = 0$

$\sf \implies 3\sec(x) = 5\tan(x)$

$\sf \implies \frac{3}{5} = \frac{\tan(x)}{ \sec(x)}$

We know that,

$\sf \cos(x) = \frac{1}{ \sec(x) }$

So,

$\sf \implies \frac{3}{5} = \tan(x) \times \cos(x)$

We know that,

$\sf \tan(x) = \frac{ \sin(x) }{ \cos(x) }$

$\sf \implies \frac{3}{5} = \frac{ \sin(x) }{ \cos(x) } \times \cos(x)$

$\sf \implies \sin(x) = \frac{3}{5}$

Hence, the value of sin(x) is 3/5 which is our required answer.

Formulae Used:

1. $\sf \tan(x) = \frac{ \sin(x) }{ \cos(x) }$
2. $\sf \cos(x) = \frac{1}{ \sec(x) }$

Answer 2

Answer:

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