Question

If sin[${90}^{\circ }$- (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 = 90^o
• C. both (a) and (b)
• D. none of these

Answer 1

The correct option is C

both (a) and (b)

sin[${90}^{\circ }$ - (A+B)] = cosx

sin[${90}^{\circ }$ - (A+B)] = cosx(A+B)

Thus, x = A+B

sin[${90}^{\circ }$ - (A+B)] = cosy

sin[${90}^{\circ }$ - (A+B)] = sin(${90}^{\circ }$ - y)

Thus, y = A+B

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

and given, A+B = ${90}^{\circ }$

Hence, y = C = A+B = ${90}^{\circ }$.