SOLUTION: verify each of the following identities pls. help me thank you. prob. 1. sin(A-B)/sinAsinB = cotB-cotA prob. 2. tan A/2 + cot A/2 = 2cscA

Algebra ->  Trigonometry-basics -> SOLUTION: verify each of the following identities pls. help me thank you. prob. 1. sin(A-B)/sinAsinB = cotB-cotA prob. 2. tan A/2 + cot A/2 = 2cscA      Log On


   

Question 420224: verify each of the following identities
pls. help me thank you.
prob. 1. sin(A-B)/sinAsinB = cotB-cotA
prob. 2. tan A/2 + cot A/2 = 2cscA
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
prob. 1. sin(A-B)/sinAsinB = cotB-cotA
prob. 2. tan A/2 + cot A/2 = 2cscA
..
1. sin(A-B)/sinAsinB = cotB-cotA
Starting with left side,
sinACosB-cosAsinB/sinAsinB
Divide both terms by sinAsinB
sinACosB/sinAsinB-cosAsinB/sinAsinB
cosB/sinB-cosA/sinA=cotB-cotA
verified: Left-hand side=right-hand side
..
2. tan A/2 + cot A/2 = 2cscA
starting with left side
tan(1/2)A=sinA/1+cosA
cot(1/2)A=reciprocal of tan (1/2)A=1+cosA/sinA
=sinA/1+cosA+1+cosA/sinA
LCD=(sinA)(1+cosA)
=sin^2A+1+2cosA+cos^2A/(sinA)(1+cosA)
=2+2cosA/(sinA)(1+cosA)
=2(1+cosA)/(sinA)(1+cosA)
=2/sinA=2cscA
verified:Left-hand side=right-hand side