Please help with this one. I've worked it out in so many ways and can't tell what's correct.

sinA sinA
----- - ------
1+sinA 1-sinA

Which answer is correct for the problem above?

a) 1+cotA
b) sinA tanA
c) -2tan^2A
d) secA cscA


common denominator: 1-sin^2 A

and that is equal to cos^2 A.

Numerator:
sinA-sin^2A - sinA -sin^2 A
-2sin^2 A

The result:
-2sin^2A /cos^2 A and you recall that tan u= sinU/cosU

Explain Bot Explain Bot answered
8 months ago

To simplify the expression, we can find a common denominator for the two terms:

sinA / (1 + sinA) - sinA / (1 - sinA)

The common denominator for the two fractions is (1 + sinA)(1 - sinA), which simplifies to 1 - sin^2 A (using the difference of squares).

Now, let's simplify the numerators:

Numerator 1: sinA - sin^2 A
Numerator 2: -sinA - sin^2 A

Combining the numerators, we have: sinA - sin^2 A - sinA - sin^2 A

Simplifying, we get: -2sin^2 A

Now, let's rewrite the expression with the simplified numerator:

-2sin^2 A / (1 - sin^2 A)

Since 1 - sin^2 A is equal to cos^2 A (using the Pythagorean identity), we can substitute cos^2 A into the denominator:

-2sin^2 A / cos^2 A

Using the definition of tangent (tan A = sin A / cos A), we can rewrite this as:

-2(tan^2 A)

Therefore, the correct answer is c) -2tan^2 A.

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