What is the answer for question 3) ?

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a) The trigonometric identities to be proved are:

a) `secx(1+cosx)=(1+secx)`

L.H.S.`=secx(1+cosx)`

`=secx+secx*cosx`

`=(secx+1)` (since `secx=1/cosx` , so `secx*cosx=1` )

=R.H.S.

b)` tanx/(secx+1)=(secx-1)/tanx`

L.H.S.`=tanx/(secx+1)`

Multiply both numerator and demnominator by `(secx-1)` , to get

`(tanx(secx-1))/((secx+1)(secx-1))`

`= (tanx(secx-1))/(sec^2x-1)`

`=(tanx(secx-1))/(tan^2x)`

`=(secx-1)/tanx ` (dividing both numerator and denominator by tanx, asssuming that `tanx!=0` )

=R.H.S.

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