Proofs for Parts 1-4 require that you only know and use the basic (fundamental) and pythagorean identities:
Prove Basic Trig Identities Part 1: http://www.youtube.com/watch?v=iKWGv0xcuCA
Prove Basic Trig Identities Part 2: http://www.youtube.com/watch?v=cqqpINKly24
Prove Basic Trig Identities Part 3: http://www.youtube.com/watch?v=h6UGBn6cD4c
Prove Basic Trig Identities Part 4: http://www.youtube.com/watch?v=2m0_HXU2AGg
Prove Trig Identity 5: http://youtu.be/PbjYiJ2Pmso
We verify a Trig identity by using the basic identities and the identity for the cosine of a sum or difference. We prove: (cos(x+y))/(cosx·cosy) = 1 - tanx·tany
Prove Trig Identity 6: http://youtu.be/QzB3cTsInpc
We verify a Trig identity by using the basic identities and the identity for the cosine of a sum or difference. We prove: (cos(x+y))/(cos(x — y) = (coty — tanx)/(coty + tanx)
Prove Trig Identity 7: http://youtu.be/PIhkiH8-3ds
We verify a Trig identity by using the basic identities and the identity for the sine of a sum or difference. We prove: (sin(x+y))/(sinx·cosy) = 1 + cotx·tany
Prove Trig Identity 8: http://youtu.be/Hyuave3UzYY
We verify a Trig identity by using the basic identities and the identity for the cosine and sine of a sum or difference. We prove: (cos(A+B))/(sin(A - B)) = (1 - tanAtanB)/(tanA - tanB)
Prove Trig Identity 9: http://www.youtube.com/watch?v=88r_tIpfmMk
We verify two identities using the double angle and half angle identities.