# If 3sinA+4cosA=5, find sinA

1
by Anniieee

2015-04-05T15:08:07+05:30

### This Is a Certified Answer

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
3/5  Sin A  + 4/5  Cos A  = 1
we see that  (3/5)² + (4/5)² = 1
let  3/5 = Sin B            and      4/5 = Cos B
So Sin A Sin B + Cos A Cos B = 1 = Cos 0°
Cos (A - B) = cos 0°
A = B    or    A - B = 2 π

if A = B,  Sin A = Sin B = 3/5.
or,  if A - B = 2π,  Sin A = Sin (2π+B) = Sin B = 3/5

=========================
alternately:

4 Cos A = 5 - 3 Sin A
16 Cos² A = 25 + 9 Sin² A - 30 Sin A
16 - 16 Sin² A = 25 + 9 Sin² A - 30 Sin A

25 Sin² A  - 30 Sin A + 9 = 0

Sin A = [ 30 +- √(900 - 900) ] / 50 = 3/5

Thanx a lot.. u helped me very much.. just one ques how did sinAsinB+ cosAcosB become cos(A-B)?
that is the formula for Cos (A - B).
Sin A Cos B + Cos A Sin B = Sin (A+B) is another formul
Kk.. thanx