Question

If 5 tan x =3, then what is the value of (5 sinx -3 cos x)/(4 sin x +3 cosx) *​

Answer 1

Answer:

5sinx+4cosx=3

Squaring both sides

25sin  

2

x+16cos  

2

x+2∗5∗4sinxcosx=9⇒9sin  

2

x+7+40sinxcosx=0

⇒9sin  

2

x+7=−40sinxcosx

Now, 4sinx−5cosx=  

(4sinx−5cosx)  

2

 

​

 

=  

16sin  

2

x+25cos  

2

x−40sinxcosx

​

 

=  

16sin  

2

x+25cos  

2

x+9sin  

2

x+7

​

=  

25sin  

2

x+25cos  

2

x+7

​

=  

25+7

​

=  

32

​

=4  

2

​

Step-by-step explanation:

Answer 2

Answer:

Step-by-step explanation:

tan x=5/3(Opposite side/Adjacent side)

In triangle ABC right angled at B,Let us assume that theta (x)=Angle A.So:

AB= 5 units

BC=3 units

So by Pythagoras theorem:

AC^2=25+9

AC= root 34

Sin x=3/root 34

Cos x=5/root 34

By substituting these values in the equation,the final answer is 0.