Question

If tanθ = 3, then what is the value of (5 sinθ - 3 cosθ/ 4sinθ + 3cosθ) ?​

Answer 1

Answer:iven,

5tanθ=3

∴tanθ=  

5

3

​  

 

Now,

4sinθ+3cosθ

5sinθ−3cosθ

​  

 

=  

4tanθ+3

5tanθ−3

​  

 [dividing numerators and denominator by cosθ]

=  

4(  

5

3

​  

)+3

5(  

5

3

​  

)−3

​  

 

=  

5

12

​  

+3

3−3

​  

 

=  

5

12

​  

+3

0

​  

 

=0

∴  

4sinθ+3cosθ

5sinθ−3cosθ

​  

=0