Question

If $si{n}^2$z = 1 + $co{s}^2$ y, find the value of $co{s}^2$ z + $si{n}^2$ y

__

Answer 1

We know 1 + $co{s}^2$y is greater than or equal to one. Also, the maximum value of $si{n}^2$ z is 1.

So we have $si{n}^2$z ≤ 1 and $si{n}^2$ z = 1 + $co{s}^2$ y ≥1

or 1 ≤ $si{n}^2$ z ≤ 1

⇒ $si{n}^2$ z = 1

⇒ $co{s}^2$ y = $si{n}^2$ z - 1 = 1 - 1 = 0

⇒ $co{s}^2$ z + $si{n}^2$ y = 0 + 1 = 1