Question

prove it.......using identities​

Answer 1

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$\huge\boxed{\fcolorbox{red}{Yellow}{Answer }}$

$\: \: \pink\bigstar \sf{ \frac{1}{ {cos}^{2} \theta } - {tan }^{2} \theta = 1 }....to \: prove$

$\: \: \red \bigstar \tt{ \frac{1}{ {cos}^{2} \theta} - {tan}^{2} \theta}$

$\: \: \red \bigstar \tt{ left \: hand \: side \to \: \frac{1}{ {cos}^{2} \theta } - {tan}^{2} \theta}$

$\: \implies \displaystyle \sf{ \frac{1}{ {cos}^{2} \theta } - \frac{ {sin}^{2} \theta}{ {cos}^{2} \theta} }$

$\: \: \implies \displaystyle \sf{ \frac{1 - {sin}^{2} \theta }{ {cos}^{2} \theta} }$

$\: \: \\ \implies \displaystyle \sf{ \frac{ {cos}^{2} \theta}{ {cos}^{2} \theta} } \: \: \: \: .........use \: property \: {sin}^{2} \theta + {cos}^{2} \theta=1$

$\: \: \implies \displaystyle \sf{ \cancel \frac{ {cos}^{2 } \theta }{ {cos}^{2} \theta} } = 1$

$\: \red \bigstar \displaystyle \sf{right \: hand \: side = 1}$

$\: \: \clubsuit \underline{ \boxed{ \bf{lhs \: = rhs \: hence \: proved}}}$