Question

Prove that (1 + cot θ -cosec θ)(1 + tan θ + sec θ) = 2

Answer 1

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

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

`(( \sin( \alpha + \cos( \alpha )^2)-1^2 ) )/( \sin( \alpha \cos( \alpha ) ) )`

`(sin^2@+cos^2@+2sin@cos@ -1)/(sin@cos@ ) \\`

`(1+2sin@cos@-1)/(sin@ cos@) \\`

`(2sin@cos@)/(sin@cos@) \\`

`2 \\`

hence proved