If 3sinx + 4cosx = 5, then 4sinx - 3cosx =....???



  1. 0

  2. -5

  3. 1/5

  4. 5


plz explain me in detail... how to do questions like this... 

3 years ago

Share

Answers : (2)

                    

ANS    3sinx+4cosx=5


     => 3/5 sinx +4/5 cosx = 1


     let cosA=3/5   => sinA=4/5


     =>  cosAsinx + sinAcosx = 1


     =>  sin(x+A) = 1


Now,


       4sinx - 3cosx


  =   5(4/5sinx - 3/5 cosx)     [multipying numerator and denominator by 5]


  =   5(sinAsinx - cosAcosx)


  =   -5{cos(x+A)} = -5[root{1-(sin(x+A)^2)}] = -5 x 0 = 0          Ans 0


 


TRICK: if asinx+bcosx is given then multiply numerator and denominator by root(a^2 +b^2)


            this method is useful  in many questions 


 


 


 PLEASE       APPROVE       MY       ANSWER       IF       YOU       LIKE       IT


 

3 years ago
                    

3sinx+4cosx=5


Squaring on both sides.


(3sinx+4cosx) 2 = 25


9sin2x +16 cos2x+24sinxcosx=25


9(1- cos2x)+16(1- sin2x)+ 24sinxcosx=25


9-9 cos2x+16-16 sin2x+24sinxcosx=25


25-9 cos2x-16 sin2x+24sinxcosx=25


9 cos2x+16 sin2x-24sinxcosx=0


(3cosx-4sinx) 2 = 0


4sinx-3cosx=0


 

one year ago

Post Your Answer

More Questions On Trigonometry

Ask Experts

Have any Question? Ask Experts
Post Question
 
Answer ‘n’ Earn
Attractive Gift
Vouchers
To Win!!!
Click Here for details
cosx+cosy-cos(x+y)=3/2
 
 
Hello Student, cosx+cosy-cos(x+y)=3/2 2cos((x+y)/2)cos((x-y)/2)-2[cos((x+y)/2))]^2-0.5=0 =>2ka-2k^2-0.5=0 =>D=4a^2-4>=0 =>a=1 since its a cos(x-y) whose value is in [-1,1] so x=y...
  img
Arun Kumar 25 days ago
Determine a such that x2-11x+a and x2-14x +2a may have a common factor.​
 
 
Hello Student, Thanks & Regards Arun Kumar Btech, IIT Delhi Askiitians Faculty
  img
Arun Kumar 26 days ago
What is the sin rule?
 
 
Hello Student, Thanks & Regards Arun Kumar Btech, IIT Delhi Askiitians Faculty
  img
Arun Kumar 26 days ago
find the length of the curve y=(1/3)(x^2+2)^3/2 ?
 
 
your question iswrong .. it must be area..!
 
Harsh davda 4 months ago
IF y=1/sin x+1/sin root over 1-xx then find dy/dx
 
 
Thanks & Regards Saurabh Singh, askIITians Faculty B.Tech. IIT Kanpur
  img
Saurabh Singh 5 months ago
 
Thanks & Regards Saurabh Singh, askIITians Faculty Btech IITK
  img
Saurabh Singh 5 months ago
a fighter plane flying horizontally at an altitude of 1.5 km with speed 720km/hr passes directly overhead an antiaircraft gun.At what angle from the vertical should the gun be fired for the...
 
 
Height of the fighter plane = 1.5 km = 1500 m Speed of the fighter plane, v = 720 km/h = 200 m/s Let θ be the angle with the vertical so that the shell hits the plane. Muzzle velocity...
 
Parth Shrivastava one year ago
 
Height of the fighter plane = 1.5 km = 1500 m Speed of the fighter plane, v = 720 km/h = 200 m/s Let θ be the angle with the vertical so that the shell hits the plane. The situation is...
 
G Ashwin - one year ago
View all Questions »