Question

if tan^4a+tan^2a=1,then show that cos^4a+cos^2a=1​

Answer 1

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Answer 2

Answer:

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$\tan {}^{4} a + \tan {}^{2} a = 1 \\ \\ = > ( \tan {}^{2} a + 1) \tan {}^{2} a = 1 \\ = > \sec {}^{2} a \tan {}^{2} a = 1 \\ = > ( \frac{1}{ \cos {}^{2} \: a } ) \tan {}^{2} a = 1 \\ = > \tan {}^{2} a = \cos {}^{2} a \\ = > \frac{ \sin {}^{2}a }{ \cos {}^{2}a } = \cos {}^{2}a \\ = > \sin {}^{2} a = \cos {}^{4} a \\ = > 1 - \cos {}^{2} a = \cos {}^{4} \\ = > \cos {}^{4} a + \cos {}^{2} a = 1$

Hence proved.

Hope it helped you.