6.3. Sum and Difference Identities http://www.ck12.org
sin(x−y)
sin(x+y)=tanx−tany
tanx+tany
sinxcosy−cosxsiny
sinxcosy+cosxsiny=
sinxcosy−cosxsiny
sinxcosy+cosxsiny·( 1
cosx·cosy)
( 1
cosx·cosy)=
(sinxcosy
cosx·cosy)
−
(cosxsiny
cosx·cosy)
(sinxcosy
cosx·cosy)
+
(cosxsiny
cosx·cosy)=
tanx−tany
tanx+tany=Practice
Find the exact value for each expression by using a sum or difference identity.
- cos 75◦
- cos 105◦
- cos 165◦
- sin 105◦
- sec 105◦
- tan 75◦
- Prove the sine of a sum identity.
- Prove the tangent of a sum identity.
- Prove the tangent of a difference identity.
- Evaluate without a calculator: cos 50◦cos 10◦−sin 50◦sin 10◦.
- Evaluate without a calculator: sin 35◦cos 5◦−cos 35◦sin 5◦.
- Evaluate without a calculator: sin 55◦cos 5◦+cos 55◦sin 5◦.
- If cosαcosβ=sinαsinβ, then what does cos(α+β)equal?
- Prove that tan(x+π 4 )=^11 +−tantanxx.
- Prove that sin(x+π) =−sinx.