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


 

2 years 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
What is the sin rule?
 
 
Hello Student, Thanks & Regards Arun Kumar Btech, IIT Delhi Askiitians Faculty
  img
Arun Kumar 5 months ago
( * ) If theta lies in the first quardrant and 5 tan theta = 4, then ( cosec square theta – sec square theta ) / (sin theta + 2 cos theta) =
 
 
Hello student, Please find the answer to your question below tan Ø = 4/5 So sinØ= 4/root{41}, cosØ= 5/root{41} You habe all the values just you have to put in eqn and...
  img
Nishant Vora 3 months ago
Prove that [cosx – sinx][cos2x – sin2x] = cosx – sin3x
 
 
Ans: Hello Student, Please find answer to your question below Hence Proved
  img
Jitender Singh 4 months ago
 
the value of cos6 sin24 cos72
 
laxman 4 months ago
 
wqwqwqwq
 
laxman 4 months ago
what is the method to find range.
 
 
Hello student, Please find the answer to your question below Method 1 of 4: Finding the Range of a Function Given a Formula 1 Write down the formula.Let's say the formula you're...
  img
SHAIK AASIF AHAMED 3 months ago
 
 
Yugabrat Gogoi 3 months ago
if abcd is a quadrilateral and e & f are midpoint of ac & bd respectively. prove that ab+ac+cb+cd = 4ef
 
 
The correct question is Since F is the midpoint of BD, we get …...(1) Similarly …....(2) Adding (1) and (2) we get Hence proved.
  img
Satyajit Samal 2 months ago
How many numbers are there between 100 and 1000 such that every digit is either 2 or 9?
 
 
Hello Student, The numbers between 100 and 1000 are clearly the three digit number. All the three digits can be filled by 2 ways. => 2*2*2 = 8 ways Thanks & Regards Arun Kumar Btech,...
  img
Arun Kumar 5 months ago
View all Questions »