Question Number 100131 by bemath last updated on 25/Jun/20

If 3sin x+4cos x=5 then sin x=?

Commented bybobhans last updated on 25/Jun/20

let tan ((x/2)) = t , ⇒sin x = ((2t)/(1+t^2 )) , cos x=((1−t^2 )/(1+t^2 )) ⇔((6t+4−4t^2 )/(1+t^2 )) = 5 ⇒−4t^2 +6t+4=5t^2 +5 9t^2 −6t+1=0 , (3t−1)^2 =0 t=(1/3) ⇒sin x=((2/3)/(1+(1/9))) = (6/(10)) = (3/5)

Commented bybemath last updated on 25/Jun/20

thank you all

Commented byDwaipayan Shikari last updated on 25/Jun/20

(3sinx+4cosx)^2 =25 9sin^2 x+24sinxcosx+16cos^2 x=25(sin^2 x+cos^2 x) 16sin^2 x−24sinxcosx+9cos^2 x=0 (4sinx−3cosx)^2 =0 or cotx=(4/3) 3+4cotx=(5/(sinx)) or ((sinx)/5)=(3/(25)) so sinx=(3/5)

Answered by Rasheed.Sindhi last updated on 25/Jun/20

If 3sin x+4cos x=5 then sin x=? 4cos x=5−3sin x 16cos^2 x=(5−3sin x)^2 16(1−sin^2 x)=25−30sin x+9sin^2 x 25sin^2 x−30sin x+9=0 sin x=((30±(√(900−900)))/(50)) =(3/5)

Answered by mr W last updated on 25/Jun/20

cos x cos α+sin x sin α=1 with sin α=(3/5), cos α=(4/5) cos (x−α)=1 x−α=2kπ x=2kπ+α sin x=sin α=(3/5)