Sin ^2 63 + sin ^ 2 27/ cos ^17 + cos^ 73 working out please

This is your question

Sin ^2 63 + sin ^ 2 27/ cos ^17 + cos^ 73

This is what I think you actually meant

(Sin ^2 (63) + sin ^ 2 (27)/ (cos ^2 (17) + cos^2 (73))

You need to be more careful - anyway

$$sin\theta = cos(90-\theta)$$   and vise versa - you can see this if you draw a right angled triangle and take a look

therefore

sin63=cos27  and cos73=sin17    so the question becomes

$$\frac{cos^2 (27)+sin^2(27)}{cos^2(17)+sin^2(17)}\\
=\frac{1}{1}\\
=1$$

 Now please say thank you.