Question

If Sin(A+B)=24/25 and Cos(A-B)=4/5 Then find Tan2A

Answer 1

The value of Tan 2A is 3/4

Step-by-step explanation:

we have to find the value of Tan 2A

given : sin (A+B) = 24/25

cos(A-B) = 4/5

then

if $\sin (A+B) =\frac{P}{H}$

i.e perpendicular is 24 and and hypotenuse is 25

by using pythagoras theorem

we will find the third side of the triangle

25² =24² +base²

on solving base = 7

therefore , $\tan (A+B) = \frac{24}{7}$

similarly $\cos (A-B) = \frac{4}{5}$

here , base = 4 , hypotenuse = 5

using pythagoras again

5² = 4²+ perpendicular ²

perpendicular = 3

then $\tan (A-B) = \frac{-3}{4}$

now ,

$\tan 2A = \tan (A+B)+ \tan (A-B)= \frac{\tan (A+B)+ \tan (A-B)}{1-\tan (A+B)\times \tan (A-B)}\\\\\tan 2A =\frac{\frac{24}{7}+(\frac{-3}{4})}{1-\frac{24}{7}\times\frac{-3}{4}}= \frac{3}{4}$

hence , The value of Tan 2A is 3/4

#Learn more:

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