Question

prove: tan inverse [ cos x / (1sin x)] = pie /4 - (x/2)​

Answer 1

$\huge{Hey Mate!!!}$

☆☞ Here is ur answer ☜☆

✔✔ = cos2(x/2) - sin2 (x/2)  / sin2(x/2)+cos2(x/2)+2 sin(x/2) cos(x/2)

✔✔ = [cos(x/2) - sin(x/2)] [cos(x/2) + sin(x/2)] / [sin(x/2)+cos(x/2)]2

✔✔ = [cos(x/2) - sin(x/2)] / [cos(x/2) + sin (x/2)]

✔✔ = 1 - tan(x/2) / 1+tan(x/2)

✔✔ = tan (pi/4 - x/2)

✔✔ =tan-1[tan(pi/4 - x/2)]

✔✔ = pi/4 - x/2

HOPE IT HELPS!

Answer 2

$<font color="violet">$hello!!!

☆☞ Here is ur answer ☜☆

» cos2(x/2) - sin2 (x/2) / sin2(x/2)+cos2(x/2)+2 sin(x/2) cos(x/2)

» [cos(x/2) - sin(x/2)] [cos(x/2) + sin(x/2)] / [sin(x/2)+cos(x/2)]2

» [cos(x/2) - sin(x/2)] / [cos(x/2) + sin (x/2)]

» 1 - tan(x/2) / 1+tan(x/2)

» tan (pi/4 - x/2)

» tan-1[tan(pi/4 - x/2)]

» pi/4 - x/2