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  • use identity sin^2 theta + cos^2 theta = 1 to prove sec^2 theta = 1 + tan^2 theta

use identity sin^2 theta + cos^2 theta = 1 to prove sec^2 theta = 1 + tan^2 theta

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\sec^2 \theta = 1 + \tan^2 \theta \\ RHS = 1 + \tan^2 \theta \\\\ = 1 + \frac{\sin^2 \theta }{\cos ^2 \theta } \\\\ = \frac{\cos^2 \theta + \sin^2 \theta }{\cos^2 \theta } \because \sin^2 \theta + \cos^2 \theta =1 \\\\ = \frac{1}{\cos ^2 \theta } \\\\ = \sec^2 \theta = LHS \\ $ Hence proved

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Ravindra Pindel

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