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

0
-5
1/5
5

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

5 years ago

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```										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

```
5 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

```
4 years ago
```										3sinx+4cosx=5.Do sqaring on both sides.The equation will be as :- 9sin2x+16cos2x+24sinx.cosx=25.Let the above equation be no.1Think 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.2Add equations no.1 and no.2You will get as :- 25sin2x+25cos2x=25+p225(sin2x+cos2x)=25+p225=25+p2                                   (because sin2x+cos2x=1)p2=0p=0.4sinx-3cosx=0.Therefore answer is 0.  PLEASE  APPROVE  MY  ANSWER  IF IT IS RIGHT
```
one year 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
```										HINT:  (3sinx +4cosx)^2+(3cosx-4sinx)^2=(3^2+4^2)(cos^2x+sin^2x)
```
one year ago
```										easiest method....given 3sinx+4cosx=5..then find 4sinx-3cosx=?a=3  b=4  c=5...let our ans to be ka^2+b^2=c^2+k^2after putting values nd solving we get...k=0...easy method...
```
7 months ago

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