Question

Complete the identity: sec(t) - cos(t) = ?

1) sec(t)csc(t)
2) -2tan²(t)
3) 1 + cot(t)
4) sin(t)tan(t)​

Answer 1

Explanation:

`\sec( \alpha ) - \cos( \alpha )`

`(1)/( \cos( \alpha ) ) - \cos( \alpha )`

`(1)/( \cos( \alpha ) ) - \frac{ \cos {}^(2) ( \alpha ) }{ \cos( \alpha ) }`

`\frac{ \sin {}^(2) ( \alpha ) }{ \cos( \alpha ) }`

`( \sin( \alpha ) )/( \cos( \alpha ) ) * ( \sin( \alpha ) )/(1)`

`\tan( \alpha ) \sin( \alpha )`

4 is the option