2tanx/1 - tan2x + 1/ 2 cos2x -1= cosx + sinx/ cosx - sinx

is proved

Solution:

Given that,

Let us first solve the L.H.S

 --- (1)

By trignometric identities,

By using these in (1) we get,

By definition of tan,

Therefore,

 --- (ii)

By trignometric identities,

By using these in (ii)

 ----- (iii)

We know that,

Similarly,

Also,

Similarly,

Therefore apply these in (iii)

Cancel out (cos x + sin x) on numerator and denominator

Thus L.H.S = R.H.S

Thus proved

1.0

step-by-step explanation: