Question

(1-tan 0)2 +(1+tan 0)2=2sec2 0​

Answer 1

$\\ \quad \dag \underline{ \sf Solving \: LHS \: part }$

$\\ \quad : \implies \sf {(1 - \tan \theta)}^{2} + {(1 + \tan \theta)}^{2}$

$\\ \quad : \implies \sf 1 + { \tan}^{2} \theta - \cancel{2 \tan \theta} + 1 + { \tan}^{2} \theta + \cancel{2 \tan \theta }$

$\\ \quad : \implies \sf 2 + 2 { \tan}^{2} \theta$

$\\ \quad : \implies \sf 2(1 + { \tan}^{2} \theta)$

$\\ \quad\therefore \boxed{ \sf 2 { \sec}^{2} \theta} \bigstar \quad \qquad \quad \qquad \qquad \bigg \{ 1 + { \tan}^{2} \theta = { \sec}^{2} \theta \bigg \}$

LHS = RHS

hence Verified!

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