Question

if tan A = 3/2 & cot B = 5/12 , find sin A . sin B - cos A . cos B

Answer 1

TanA=3/2

By Applying Pythagoras theorem .... (Image 1)

The hypotenuse = √13

Therefore...

SinA=3/√13 and. cosA=2/√13

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CotB=5/12

Applying Pythagoras theorem...(Image 2)

The hypotenuse =13

Therefore...

SinB=12/13. and cosB=5/13

Hence!

=SinA*sinB-cosA*cosB

= 3/√13*12/13 - 2/√13*5/13