Question

If 3 sin + 5 cos = 5 , ℎ ( 3 cos − 5 sin ) 2 ​

Answer 1

Answer:

Answer

Given 3sinθ+5cosθ=5

Let 5sinθ−3cosθ=x

Squaring on both sides for both the equations

⇒9sin

2

θ+25cos

2

θ+30sinθcosθ=25

⇒25sin

2

θ+9cos

2

θ−30sinθcosθ=x

2

Adding the equations ;

⇒34(sin

2

θ+cos

2

θ)=25+x

2

⇒x

2

=34−25=9

⇒x=±3

∴5sinθ−3cosθ=±3

Hence proved.

Step-by-step explanation:

Answer 2

Answer:

Given:

(3 sin0+5cos0)²= 5²

Squaring on both sides.

(3sin0)²+(5cose)²+2× 3sine 5cos0= 25

[a+b=a²+b²+2ab]

9sin²0+ 25cos²0+30sin0cos0= 25

9 (1-cos²0) + 25(1-sin²0)+30sincos0=25

[sin²0 + cos²0 =1]

9-9cos²0 +25-25sin²0 +30sin0cos0=25

9+25 -(9cos²0 +25sin²0 -30sin cose)

=25

34 - (9cos²0 +25sin²0 -30sinecos0) =25

- (25sin²0 +9cos²0-30sincos0) =25-34

(25sin²0+9cos²0 -30sin cose) =9

(5sine - 3cos0)²= 9

(5sin0 - 3cose)= √9

(5sin0 - 3cos0)= +3

L.H.S R.H.S