SOLUTION: pls. help me solve this problem.. thank you so much. verify each of the following identity: 1. sin ( pi/2 + A) = cosA 2. sin (A+B) / sin (A-B)=tanA + tanB /tanA-tanB

Algebra ->  Trigonometry-basics -> SOLUTION: pls. help me solve this problem.. thank you so much. verify each of the following identity: 1. sin ( pi/2 + A) = cosA 2. sin (A+B) / sin (A-B)=tanA + tanB /tanA-tanB      Log On


   

Question 421510: pls. help me solve this problem.. thank you so much.
verify each of the following identity:
1. sin ( pi/2 + A) = cosA
2. sin (A+B) / sin (A-B)=tanA + tanB /tanA-tanB
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
1. sin ( pi/2 + A) = cosA
2. sin (A+B) / sin (A-B)=tanA + tanB /tanA-tanB
.
1.sin(pi/2+A)=cosA
starting with left side
using sin addition formula and following identities
cos pi/2=0
sin pi/2=1
sin(pi/2+A)=sinpi/2cosA+cospi/2sinA
=(1)cosA+(0)sinA
=cosA
verified: left side=right side
..
2.sin(A+B)/sin(A-B)=tanA+tanB/tanA-tanB
starting with right side
tanA+tanB/tanA-tanB
=[(sinA/cosA)+(sinB/cosB)]/[(sinA/cosA)-(sinB/cosB)]
LCD=cosAcosB
=[(sinAcosB)+(cosAsinB)]/[(sinAcosB)-(cosA/sinB)]
=sin(A+B)/sin(A-B)
verified: right side=left side