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Grade: 10
        
Sintheta +2Costheta= 1 then prove that 2sintheta-costheta=2
4 months ago

Answers : (2)

Aditya Gupta
1236 Points
							
let 2sintheta-costheta= k
Sintheta +2Costheta= 1
squaring and adding,
5= 1+k^2
k^2=4
so k=2
or 2sintheta-costheta= 2
 
 
4 months ago
Arun
21584 Points
							

sin ϴ + 2 cos ϴ = 1

Squaring both the sides

(sin ϴ + 2 cos ϴ) ² = (1) ²

sin² ϴ + 4 cos² ϴ + 4 sin ϴ cos ϴ = 1

because sin² ϴ = 1 - cos² ϴ & cos² ϴ=1- sin² ϴ

So replacing sin² ϴ by 1 - cos² ϴ and cos² ϴ by 1- sin² ϴ

we get

1 - cos² ϴ + 4 ( 1 - sin² ϴ ) + 4sin ϴ cos ϴ = 1

1 - cos² ϴ + 4 – 4sin² ϴ + 4 sin ϴ cos ϴ = 1

5 – 1 = cos² ϴ +4sin² ϴ - 4 sin ϴ cos ϴ

or

( cos ϴ – 2 sin ϴ ) ² = 4

cos ϴ -2sin ϴ = ± 2 or simply 2 ignoring -2

4 months ago
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