Question

If sin[90 - (A+B)] = cosx = cosy, then find the value of x and y; if y is the angle C of triangle ABC.
(In triangle ABC, A + B = ${90}^{\circ }$)

Answer 1

sin[90 - (A+B)] = cosx

sin[90 - (A+B)] = sin(90 - x)

Thus, x = A+B

sin[90 - (A+B)] = cosy

sin[90 - (A+B)] = sin(90 - y)

Thus, y = A+B

Also, In triangle ABC, A+B+C = ${180}^{\circ }$

and given, A+B = ${90}^{\circ }$ and y = angle C of triangle ABC,

Hence, y = C = ${90}^{\circ }$

Also, x = A+B = y = ${90}^{\circ }$