Total Price:

There are no items in this cart.
Continue Shopping

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


Answers : (4)


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


       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


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



2 years ago
                                        3sinx+4cosx=5Squaring on both sides.(3sinx+4cosx) 2 = 259sin2x +16 cos2x+24sinxcosx=259(1- cos2x)+16(1- sin2x)+ 24sinxcosx=259-9 cos2x+16-16 sin2x+24sinxcosx=2525-9 cos2x-16 sin2x+24sinxcosx=259 cos2x+16 sin2x-24sinxcosx=0(3cosx-4sinx) 2 = 04sinx-3cosx=0
20 hours ago
Do sqaring on both sides.
The equation will be as :- 9sin2x+16cos2x+24sinx.cosx=25.
Let the above equation be no.1
Think that the value of 4sinx-3cosx=p.
Do squaring on both sides.
The eqation will be as :- 16sin2x+9cos2x-24sinx.cosx=p2.
Let the above equation be no.2
Add equations no.1 and no.2
You will get as :- 25sin2x+25cos2x=25+p2
25=25+p2                                   (because sin2x+cos2x=1)
Therefore answer is 0.
19 hours ago

Post Your Answer

More Questions On Trigonometry

Ask Experts

Have any Question? Ask Experts

Post Question

Answer ‘n’ Earn
Attractive Gift
To Win!!!
Click Here for details
solve for x sin3x *sin(cube) x +cos3x *cos(cube) x=0
Hello Student, sin3x *sin^3 x +cos3x *cos^3 x=0 tan3x*tan^3x=0 =>tan3x=0 union tan^3x=0 =>3x=n*pi union x=n*pi
Arun Kumar 10 months ago
please give some easy method as i am in class 11 th this iss going above my head or can u just explain it
rashmi 10 months ago
solve cot theta - tan theta - costheta +sintheta = 0
Ans:Hello student, please find answer to your question One solution is: Second solution is
Jitender Singh 10 months ago
If 3(siny – cosx) = 4(sinx + cosy), prove that sin3x / cos3y = 1
Ans:Hello student, please find answer to your question
Jitender Singh 10 months ago
Can you please explain how did you get the last step?
Y RAJYALAKSHMI 10 months ago
is there any formula for the lenght of the intercept made by any circle on a line ?
Yes, Length of intercept made by circle on a line = 2(r 2 - p 2 ) 1/2 where r = radius of circle, p = perpendicular distance from centre to the line
Himaja 5 months ago
Yes, Length of intercept made by circle on a line = 2(r 2 - p 2 ) 1/2 where r = radius of circle, p = perpendicular distance from centre to the line
Himaja 5 months ago
plz. answer the attached question of probability. and also name the rule or theorem that will be used. thanks.
hii You can use Baye’s Theorem of Probability in order to solve this question
Sourabh Singh one month ago
I tried using bayes theorem but there is a little confusion.if u can plz tell me the value of P(E1) and P(E2) P(A/E1) and P(A/E2) it will be of great help. also tell which is the correct...
sufi digital one month ago
could anyone explain me exponential and logarithmic series and tautology part from mathematical giving suitable eamples...
mansi , dont waste ur time on understanding the series expansion ,u have to just learn it ,as they are useful in specific types of questions , but u can also solve them by using lhospital...
ng29 7 days ago
hey mansi dont get disappointed and depressed , just chill and aim high to get good score u have 2 days just revise the syllabi and focus on ur weak areas revise organic and inorganic...
ng29 7 days ago
if u think that ur notes are to the point and sufficient for ur exam as u had done arihant or can check from askiitians also if they are helpful for u i am mentioning some books if u have...
ng29 7 days ago
View all Questions »