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Official 2021 Paper 2 · Q5

Paper 2Algebra

On which line is the first error in the following argument?

Asin⁡2x+cos⁡2x=1\sin^2x+\cos^2x=1 for all values of xx.
BTherefore cos⁡x=1−sin⁡2x\cos x=\sqrt{1-\sin^2x} for all values of xx.
CHence 1+cos⁡x=1+1−sin⁡2x1+\cos x=1+\sqrt{1-\sin^2x} for all values of xx.
DThus (1+cos⁡x)2=(1+1−sin⁡2x)2(1+\cos x)^2=\left(1+\sqrt{1-\sin^2x}\right)^2 for all values of xx.
ESubstituting x=πx=\pi gives 0=40=4.

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