Question

Ca
${?}^{2}$
cossquaretheta(1+ tan²theta) = 1​

Answer 1

Step-by-step explanation:

$cos {}^{2} \alpha (1 + {tan}^{2} \alpha ) \\ \\ = {cos}^{2} \alpha + {cos}^{2} \alpha \times {tan}^{2} \alpha \\ \\ = {cos}^{2} \alpha + {cos}^{2} \alpha \times \frac{ {sin}^{2} \alpha }{ {cos}^{2} \alpha } \\ \\ = {cos}^{2} \alpha + {sin}^{2} \alpha \\ \\ = 1 \: \: \: (proved) \\ \\ \\ using \: formula \: \: tan \alpha = \frac{sin \alpha }{cos \alpha } \\ \\ {sin}^{2} \alpha + {cos}^{2} \alpha = 1$