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cos 2x = cos^{2}x-sin^{2}x

1 = cos^{2}x+sin^{2}x

By adding the two equations

By substracting the two equations

sin^{2}x+cos^{2}x = 1

By deviding both sides of the equation by cos^{2}x

tan^{2}x + 1 = sec^{2}x