Question

(1-sin^2(270+a))/(1-sin^2(180+a))

Answer 1

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Answer 2

To simplify the expression (1 - sin²(270 + a))/(1 - sin²(180 + a)), let's break it down step by step.

First, we'll simplify the trigonometric functions:

sin(270 + a) = sin(270)cos(a) + cos(270)sin(a) = -cos(a) sin(180 + a) = sin(180)cos(a) + cos(180)sin(a) = -sin(a)

Now, we substitute these values back into the original expression:

(1 - sin²(270 + a))/(1 - sin²(180 + a)) = (1 - (-cos(a))²)/(1 - (-sin(a))²) = (1 - cos²(a))/(1 - sin²(a))

Using the trigonometric identity cos²(a) + sin²(a) = 1, we can simplify further:

(1 - cos²(a))/(1 - sin²(a)) = sin²(a)/(1 - sin²(a))

Therefore, the simplified expression is sin²(a)/(1 - sin²(a)).