Question

Sin2a-2cosa/ sina-sin^2a

Answer 1

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Answer 2

To simplify the expression (sin(2a) - 2cos(a)) / (sin(a) - sin^2(a)), we can use trigonometric identities.

Let's start by expressing sin(2a) in terms of sin(a) and cos(a) using the double-angle formula:

sin(2a) = 2sin(a)cos(a)

Now substitute this into the numerator of the expression:

(sin(2a) - 2cos(a)) = (2sin(a)cos(a) - 2cos(a))

Now let's simplify the denominator using the identity sin^2(a) = 1 - cos^2(a):

(sin(a) - sin^2(a)) = sin(a) - (1 - cos^2(a)) = sin(a) - 1 + cos^2(a)

Combining the simplified numerator and denominator, we have:

[(2sin(a)cos(a) - 2cos(a))] / [sin(a) - 1 + cos^2(a)]

Factoring out 2cos(a) from the numerator:

[2cos(a)(sin(a) - 1)] / [sin(a) - 1 + cos^2(a)]

Now, we can cancel out the common factor of (sin(a) - 1) in the numerator and denominator:

[2cos(a)] / [1 + cos^2(a)]

Therefore, the simplified expression is 2cos(a) / (1 + cos^2(a)).