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Question

In ABC, B=90.

If tan A=13, then

sin A.cos C+cos A.sin C = ___

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Solution

In ABC, B=90.

If tan A=13, then

sin A.cos C+cos A.sin C = ___
Given tan A=13, and B=90 in ABC.

We know that tan 30=13

A=30

Now, A+B+C=180

C=180AB=1803090=60

Now, sin A=sin 30=12

cos A=cos 30=32

sin C=sin 60=32

cos C=cos 60=12
Thus, sinAcosC+cosAsinC=12×12+32×32

=14+34=44=1

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