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# Evaluate 1 + sin x /1-sin x

Trignometric ratios is the study of the relation between the sides and angles of a right-angled triangle.

## Answer: (1+sinx) /(1-sinx) =(sec x + tan x )^{2}

Let see, how we can solve

**Explanation:**

To evaluate: (1+sin) /(1-sinx)

We will multiply and divide the expression ( 1+sin) /(1-sinx) by (1 + sinx)

Thus, we get

(1 + sinx) (1 + sinx) / (1 – sinx) (1 + sinx) ,

=(1 + sinx)^{2} /(1 - sin^{2}x) ------------- (1) ( By using identity (a-b) (a+b) = (a^{2}-b^{2}))

As we know that,

sin^{2}x + cos^{2}x = 1

So, we can write it as

1 – sin^{2}x = cos^{2}x

Replacing the denominator of (1) we get,

= (1 + sin x)^{2} / cos^{2}x

= ( (1 + sin x) / cos x) ^{2}

= ( 1/cos x + sin x/cos x)^{2}

We know that, 1/cosx = sec x and sin x/cos x = tan x

Thus, we have

= (sec x + tan x )^{2}

### Thus, 1 + sin x /1-sin x= (sec x + tan x )^{2}

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