Question

Which of the following is equivalent to the

given expression? *
(1 + sin a/1 - sin a) - (1 – sin a/1 + sin a)

Answer 1

Solution given:

`(1 + \sin( \alpha ) )/(1 - \sin( \alpha ) ) - (1 - \sin( \alpha ) )/(1 + \sin( \alpha ) )`

`\frac{(1 + \sin( \alpha )) {}^(2) - (1 - \sin( \alpha ) {}^(2) }{1 - \sin{}^(2) \alpha }`

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

`\frac{4 \sin( \alpha ) }{ \cos {}^(2)( \alpha ) }`

`4 \tan( \alpha ) \sec( \alpha )`

is your answer.