Question

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

• A. x = A+B; y=C
• B. x=A+B; y =
• C. both (a) and (b)
• D. none of these

Answer 1

The correct option is C

both (a) and (b)

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

Now, in triangle ABC, A+B+C = ${180}^{\circ }$

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

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

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