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हा 0 +2cos 6 =1 provethat 2 sin 6~ cos 6 = 2. |
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Answer» Sinθ+2cosθ=1Squaring both sides,sin²θ+2.sinθ.2cosθ+4cos²θ=1or, (1-cos²θ)+4sinθcosθ+4(1-sin²θ)=1 [∵, sin²θ+cos²θ=1]or, 1-cos²θ+4sinθcosθ+4-4sin²θ=1or, -4sin²θ+4sinθcosθ-cos²θ=1-1-4or, -(4sin²θ-4sinθcosθ+cos²θ)=-4or, (2sinθ)²-2.2sinθcosθ+(cosθ)²=4or, (2sinθ-cosθ)²=2²or, 2sinθ-cosθ=2 (Proved) |
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