Question

Need help with this​

Answer 1

$\cos \beta + \sin \beta \tan \beta \\\\= \cos \beta + (\tan \beta \cos \beta) \tan \beta \\\\=\cos \beta + \tan^2 \beta \cos \beta \\\\=\cos \beta( 1+ \tan^2 \beta)\\\\= \cos \beta \sec^2 \beta\\\\= \dfrac 1{\sec \beta} \times \sec^2 \beta \\\\= \sec \beta$

Answer 2

Step-by-step explanation:

$\cos( \beta ) + \sin( \beta ) \tan( \beta ) = \sec( \beta )$

$\cos( \beta ) + \sin( \beta ) \frac{ \sin( \beta ) }{ \cos( \beta ) }$

$\cos( \beta ) + \frac{ \sin {}^{2} ( \beta ) }{ \cos( \beta ) }$

$\frac{ \cos {}^{2} ( \beta ) }{cos \beta } + \frac{ \sin {}^{2} ( \beta ) }{ \cos( \beta ) }$

$\frac{1}{ \cos( \beta ) }$

$= \sec( \beta )$