Question

Simplify expression cos^2(pi/2-x) / √1-sin^2(x) =

Answer 1

`(cos^2((\pi)/(2)-x))/(√(1-sin^2(x)))=(sin^2(x))/(|cos(x)|)`

Explanation:

To simplify this expression you must use the following trigonometric identities

`cos((\pi)/(2)-x) = sinx` I

`1-sin (x) ^ 2 = cos ^ 2(x)` II

Remember that

`√(f(x)^2) =f(x)`

Only if
`f(x)> 0` for all x

If f(x) is not greater than 0 for all x then

`√(f(x)^2) =|f(x)|`

Now we have the expression:

`(cos^2((\pi)/(2)-x))/(√(1-sin^2(x)))`

then using the trigonometric identities I and II we have to:

`(cos^2((\pi)/(2)-x))/(√(1-sin^2(x)))=(sin^2(x))/(√(1-sin^2(x)))\\\\\\(sin^2(x))/(√(1-sin^2(x)))= (sin^2(x))/(√(cos^2(x)))`

`cos(x)` is not greater or equal than 0 for all x. So.

`(sin^2(x))/(√(cos^2(x)))=(sin^2(x))/(|cos(x)|)`

Finally

`(cos^2((\pi)/(2)-x))/(√(1-sin^2(x)))=(sin^2(x))/(|cos(x)|)`