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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)


A

x = A + B; y = C

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B

x = A + B; y = 90o

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C

both (a) and (b)

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D

none of these

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Solution

The correct option is C

both (a) and (b)


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

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

Thus, x = A+B

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

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

Thus, y = A+B

In triangle ABC, A+B+C = 180

and given, A+B = 90

Hence, y = C = A+B = 90.


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