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

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

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

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