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  • If tan A = 3 by 4 , then sinAcos A = 12 by 25 .

If tan A = 3/4 , then show that sinAcos A = 12/25 .

Answers (1)

Given:- 

\tan A= \frac{3}{4}   
To prove:-

sin A\cos A= \frac{12}{25}...........(1)        

we know that

\tan \theta = \frac{P}{B}
\frac{P}{B}= \frac{3}{4}
P=3, B = 4
Using Pythagoras theorem
H^{2}= B^{2}+P^{2}
H^{2}= \left ( 4^{2} \right )+\left ( 3^{2} \right )
H^{2}= 9+16
H^{2}= 25
H= \sqrt{25}= 5
H = 5
we know that

\sin \theta = \frac{P}{H},\cos \theta = \frac{B}{H}
Hence

\sin A= \frac{3}{5},\cos A= \frac{4}{5}
Put the value of sinA and cosA in equation (1)

\frac{3}{5}\times \frac{4}{5}= \frac{12}{25}
L.H.S. = R.H.S.
Hence proved.

Posted by

infoexpert27

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