Question

Need help with this
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Answer 1

Explanation:

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

`\cos( \beta ) + \sin( \beta ) ( \sin( \beta ) )/( \cos( \beta ) )`

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

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

`(1)/( \cos( \beta ) )`

`= \sec( \beta )`

Answer 2

`\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\\\\= \frac 1{\sec \beta} * \sec^2 \beta \\\\= \sec \beta`