6.4. Double, Half, and Power Reducing Identities http://www.ck12.org
Practice
Prove the following identities.
sin 2x=2 sinxcosx
cos 2x=cos^2 x−sin^2 x
tan 2x= 1 2 tan−tanx (^2) x
cos^2 x=^1 +cos 2 2 x
tan^2 x=^11 −+cos 2cos 2xx
sinx 2 =±
√
1 −cosx
2- cosx 2 =±
√
1 +cosx
2- tanx 2 =±
√
1 −cosx
1 +cosx- csc 2x=^12 cscxsecx
- cot 2x=cot2 cot^2 x−x^1
Find the value of each expression using half angle identities. - tan 15◦
- tan 22. 5 ◦
- sec 22. 5 ◦
- Show that tanx 2 =^1 −sincosxx.
- Show that tanx 2 = 1 +sincosxx.