Question

integral cos 2x-1/cos 2x+1 dx = ??​

Answer 1

Answer:

[Tanx-x]

Step-by-step explanation:

(Note:tan^(2)x is tan(square)x similarly with sin,cos and sec)

=∫ (1-Cos2x/1+Cos2x)dx

=∫(2Sin^(2)x/2cos^(2)x)dx

=∫ tan^(2)x dx

=∫  (sec^(2)x-1)dx  (since Tan^(2)x=Sec^(2)x-1)

=∫ sec^(2)x dx-∫ 1 dx

={Tanx-x]     (since ∫ sec^(2)x dx =Tan x)

Therefore ∫ (1-cos2x/1+cos2x)dx=[Tanx-x]