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
how to practice
 
 
Ans: Hello Student, Please find answer to your question below First, you need to remember all the trigonometric formulas & identities. Remember upto 3x. thats enough. Then, learn &...
  img
Jitender Singh 3 months ago
 
iwant the best books for jee for mathematics
 
HARSHITH one month ago
If theta is acute and (1-a square) sin theta = (1+a square) cos theta, then sin theta =
 
 
Hello student, Please find the answer to your question below (1-a 2 ) sinØ = (1+a 2 ) cos Ø tanØ = (1+a 2 )/(1-a 2 ) So , sinØ = (1+a 2 )/ root{(1+a 2 ) 2 +(1-a 2...
  img
Nishant Vora one month ago
(*) If tan A =(x sin B )/(1-xcosB) and tan B =( y sin A) / (1-y cos A) then sin A / sin B =
 
 
tanA = xsinB/(1 – xcosB) = > cotA = (1 – xcosB)/xsinB = 1/xsinB – cotB cotA + cot B = 1/xsinB …......(1) tanB = ysinA / (1 – ycosA) => cotB = (1 – ycosA)/ysinA = 1/ysinA – cotA cotB + cotA =...
 
Y RAJYALAKSHMI 2 months ago
A bullet loses nth fraction of its velocity while passing through a sandbag. The minimum number of sandbags required to arrest the bullet is?
 
 
the velocity after first bag = v- v/n = v(n-1)/n the velocity after secnod bag = v(n-1)/n- v(n-1)/n^2 = v(n-1)/n(n-1)/n = v(n-1) 2 /n 2 if n=1, means velocity loses complete velocity then 1...
  img
Sher Mohammad 3 months ago
sir what is parallelopiped this is asked in the mathematics exercise of 8 th grade but it is nowhere to be found in the book
 
 
In geometry, a parallelepiped is a three-dimensional figure formed by six parallelograms (the term rhomboidis also sometimes used with this meaning). By analogy, it relates to a...
  img
Sourabh Singh 2 months ago
 
a parallelepiped is a three-dimensional figure formed by six parallelograms. The rectangular cuboid (six rectangular faces), cube (six square faces), and the rhombohedron (six rhombus faces)...
  img
Yash Baheti 2 months ago
Let the harmonic mean and geometric mean of two positive numbers be the ratio 4 : 5. Then the two number are in the ratio=
 
 
Hello Student, Please solve for t Thanks & Regards Arun Kumar Btech, IIT Delhi Askiitians Faculty
  img
Arun Kumar 3 months ago
View all Questions »