prove the identity tan(x/2)+cot(x/2)= 2secx?

0 ⤊

prove the identity tan(x/2)+cot(x/2)= 2secx?

been stuck for a while

2007-10-31 10:13:05 · 3 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics

3 answers

sin(x/2)/cos(x/2)+cos(x/2)/sin(x/2)
tking LCM u get
sin^2(x/2)+cos^2(x/2)/sin(x/2)cos(x/2)
1/sin(x/2)cos(x/2)
1/(cosx)/2
2/cosx
2secx

2007-10-31 10:25:37 · answer #1 · answered by Siva 5 · 0⤊ 1⤋

Let x/2 = a
LHS
sin a / cos a + cos a / sin a
(sin ² a + cos ² a) / (sin a cos a)
1 / sin a cos a
1 / (sin x/2 cos x/2)
2 / (2 sin x/2 cos x/2)
2 / sin x
2 sec x

RHS
2 sec x

LHS = RHS

2007-10-31 12:01:34 · answer #2 · answered by Como 7 · 0⤊ 1⤋

tan(x/2)+cot(x/2)
= cot(x/2)[tan^2(x/2) + 1]
= cot(x/2)sec^2(x/2)
= 2/[2sin(x/2)cos(x/2)]
= 2/cosx
= 2secx

2007-10-31 10:20:34 · answer #3 · answered by sahsjing 7 · 0⤊ 1⤋