Question

Se 0 < a < π/2 e tg a= 21/20, então cos a é igual a:

Answer 1

$\tan {}^{2} ( \alpha ) + 1 = \sec {}^{2} ( \alpha ) \\ \\ ( \frac{21}{20} ) {}^{2} + 1 = \frac{1}{ \cos {}^{2} ( \alpha ) } \\ \\ \frac{441}{400} + 1 = \frac{1}{ \cos {}^{2} ( \alpha ) } \\ \\ \frac{441 + 400}{400} = \frac{1}{ \cos {}^{2} ( \alpha ) } \\ \\ \frac{841}{400} = \frac{1}{ \cos {}^{2} ( \alpha ) } \\ \\ 841 \cos {}^{2} (\alpha ) = 400 \\ \\ \cos {}^{2} ( \alpha ) = \frac{400}{841} \\ \\ \cos( \alpha ) = \sqrt{ \frac{400}{841} } \\ \\ \cos( \alpha ) = \frac{20}{ 29 }$