,showthat+86. If sin θ + 2 cos θ-1 prove that 2 sin θ-cos θ-2.INCE

1.	,showthat+86. If sin θ + 2 cos θ-1 prove that 2 sin θ-cos θ-2.INCERT EXE
Answer» 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

,showthat+86. If sin θ + 2 cos θ-1 prove that 2 sin θ-cos θ-2.INCERT EXE

Answer»

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

( cos ϴ – 2 sin ϴ ) ² = 4

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