Question - 7:(a)It' sin θ + 2 cos θ1, prove that cos θ-2 sino-2

1.	Question - 7:(a)It' sin θ + 2 cos θ1, prove that cos θ-2 sino-2
Answer» sinθ+2cosθ=1 Squaring both sides, sin²θ + 2sinθ2cosθ + 4 cos²θ = 1 (1-cos²θ)+4sinθcosθ+4(1-sin²θ)=1 [∵sin²θ + cos²θ = 1] 1- cos²θ + 4sinθcosθ + 4 - 4sin²θ=1 -4sin²θ + 4sinθcosθ - cos²θ = 1-1-4 -(4sin²θ-4sinθcosθ+cos²θ)=-4 (2sinθ)²-2.2sinθcosθ+(cosθ)²=4 (2sinθ-cosθ)²=2² 2sinθ-cosθ=2

Answer»

sinθ+2cosθ=1

Squaring both sides,

sin²θ + 2sinθ2cosθ + 4 cos²θ = 1

(1-cos²θ)+4sinθcosθ+4(1-sin²θ)=1 [∵sin²θ + cos²θ = 1]

1- cos²θ + 4sinθcosθ + 4 - 4sin²θ=1

-4sin²θ + 4sinθcosθ - cos²θ = 1-1-4

-(4sin²θ-4sinθcosθ+cos²θ)=-4

(2sinθ)²-2.2sinθcosθ+(cosθ)²=4

(2sinθ-cosθ)²=2²

2sinθ-cosθ=2

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