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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 =90

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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)] = 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

and given, A+B = 90 and y = angle C of triangle ABC,

Hence, y = C = 90

Also, x = A+B = y = 90


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