Question

3sinx+4cosx=5 solve it

Answer 1

3/5sinx+4/5cosx=1
cos53sinx+sin53cosx=1
sin(53+x)=1
53+x=90
x=37 degree

Answer 2

Answer:

Zero

Step-by-step explanation:

Given : Expression $3\sin x+4\cos x=5$

To find : The solution of the given expression?

Solution :

$3\sin x+4\cos x=5$

Squaring on both sides,

$(3\sin x+4\cos x)^2=5^2$

$9\sin^2x+16\cos^2x+24\sinx\cosx=25$ ....equation 1

Let, $4\sin x-3\cos x=p$

Squaring on both sides,

$16\sin^2x+9\cos^2x-24\sinx\cosx=p^2$ ....equation 2

Add equation 1 and 2

$25\sin^2x+25\cos^2x=25+p^2$

$25(\sin^2x+\cos^2x)=25+p^2$

$25=25+p^2$

$p^2=0$

$p=0$

i.e, $4\sin x-3\cos x=0$

Therefore, Answer is 0.