Question

1-sin^2x / sin^2x + cos^2x

Answer 1

The question asks to simplify a trigonometric expression using identities. By applying the Pythagorean trigonometric identity, sin^2x + cos^2x = 1, the expression simplifies to cos^2x.

Step-by-step explanation:

The student's question, 1-sin2x / sin2x + cos2x, involves simplifying a trigonometric expression. We know from the Pythagorean trigonometric identity that sin2x + cos2x = 1. Therefore, we can rewrite the expression by replacing the denominator with 1, resulting in:

1 - sin2x = cos2x

Now the expression simplifies to:

cos2x / 1 = cos2x

Thus, the simplified form of the original expression is cos2x. This uses the fundamental properties of trigonometric identities to simplify the expression.

Answer 2

Solution answer is
`cos^2x`

Step-by-step explanation:

`1-sin^2x  = cos^2x`

`sin^2x + cos^2x = 1`

then

`1-sin^2x / sin^2x + cos^2x = cos^2x / 1`

So

Solution answer is
`cos^2x`