Question

tan 2x/1+sec 2x = tanx

Answer 1

HEYA,

HERE IS YOUR ANSWER

(tan2x)/(1+sec2x))= tanx 
LHS =(tan2x)/(1+sec2x)) 
{sin2x/cos2x}/{1+1/cos2x} Since sec2x=1/cos2x 
={sin2x/cos2x}/{(cos2x+1)/cos2x} Taking LCM
={(sin2x)/(cos2x+1).......... Canceling out cos2x
=(2sinxcosx)/(2cos²x−1+1).......Using cos2x=2cos²x−1 
=(sinxcosx)/(cos²x)..........Canceling out cosx 
=(sinx)/(cosx)=tanx=RHS

Answer 2

Answer:

Hence proved

Step-by-step explanation:

(tan2x)/(1+sec2x))= tanx  

LHS =(tan2x)/(1+sec2x))  

{sin2x/cos2x}/{1+1/cos2x} Since sec2x=1/cos2x  

={sin2x/cos2x}/{(cos2x+1)/cos2x} Taking LCM

={(sin2x)/(cos2x+1).......... Canceling out cos2x

=(2sinxcosx)/(2cos²x−1+1).......Using cos2x=2cos²x−1  

=(sinxcosx)/(cos²x)..........Canceling out cosx  

=(sinx)/(cosx)=tanx=RHS