Question

prove that root 1+cos theta/1-cos theta -root 1-cos theta/1+cos theta=2cot theta​

Answer 1

Step-by-step explanation:

on rationalising denominators of each term

we get squareroot of (1+cosA )^2 divided by 1-cos^2A

we know that 1-cos^2A =sin^2A

then first term=1+casA divided by sinA

similarly on simplyfying 2nd term we get sinA divided by 1+cosA on subtraction we get (1+cosA)^2-sin^2Adivided by sinA(1+cosA)

on simplyfying 2cos(1+cosA) divided by sinA (1+cosA)

on canceling 2×cosA÷sinA Which is equal to 2cotA