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Question

In ABC, if B=90, tanA=13, then sinA cosC+cosA sinC=

A
1
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B
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C
3
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Solution

The correct option is A 1
Given tan A=13, and B=90 in ABC.

We know that tan 30=13

A=30

Now, A+B+C=180

C=180BA=1803090=60

Now, sin A=sin 30=12

cos A=cos 30=32

sin C=sin 60=32

cos C=cos 60=12

The first expression is sin A cos C + cos A sin C

=12×12+32×32

=14+34=44=1

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