Rumus Identitas Trigonometri (sum Difference formulas)

Pembuktian Rumus Fungsi trigonometri Untuk Jumlah dan selisih Dua Sudut
sin (α+β) = sin α.cos β + cos α.sin β (Cari di Google)
sin (α-β) = sin α.cos β - cos α.sin β (Cari di Google)
cos (α+β) = cos α.cos β - sin α.sin β (Cari di Google)
cos (α-β) = cos α.cos β + sin α.sin β (Cari di Google)
tan (α+β) = sin(α+β)/cos (α+β)
                = {sin α.cos β + cos α.sin β}/{cos α.cos β - sin α.sin β}
                = {([sin α.cos β + cos α.sin β]/[cos α.cos β - sin α.sin β]) x ([1]/[cos α.cos β]/[1]/[cos α.cos β])}
                = {([sin α.cos β + cos α.sin β]/[cos α.cos β])/([cos α.cos β - sin α.sin β]/[cos α.cos β])}
                = {([sin α.cos β/cos α.cos β]+[cos α.sin β/cos α.cos β]) / ([cos α.cos β/cos α.cos β] - [sin α.sin β/cos α.cos β])} 
                =  {[sin α/cos α]+[sin β/cos β]}/{[sin α/cos α]-([sin α/cos α][sin β/cos β])}
tan (α+β) = {tan α + tan β}/{1 - tan α.tan β}
tan (α-β) = sin(α-β)/cos (α-β)
                = {([sin α.cos β - cos α.sin β]/[cos α.cos β + sin α.sin β])               
                = {([sin α.cos β - cos α.sin β]/[cos α.cos β + sin α.sin β]) x ([1]/[cos α.cos β])/([1]/[cos α.cos β])}
               = {([sin α.cos β - cos α.sin β]/[cos α.cos β])/([cos α.cos β + sin α.sin β]/[cos α.cos β])}
                = {([sin α.cos β/cos α.cos β] - [cos α.sin β/cos α.cos β])/([cos α.cos β/cos α.cos β] + [sin α.sin β/cos α.cos β])}
               =  {[sin α/cos α]-[sin β/cos β]}/{[sin α/cos α]+([sin α/cos α][sin β/cos β])}
tan (α-β) = {tan α - tan β}/{1 + tan α.tan β}
cotan (α+β) = cos(α+β)/sin (α+β)
                     = [cos α.cos β - sin α.sin β]/[sin α.cos β + cos α.sin β]
                     = {([cos α.cos β - sin α.sin β]/[sin α.cos β + cos α.sin β]) x ([1]/[sin α.sin β]/[1]/[sin α.sin β])}
                    = {([cos α.cos β - sin α.sin β]/[sin α.sin β])/([sin α.cos β + cos α.sin β][sin α.sin β])}
                    = {([cos α.cos β/sin α.sin β]-[sin α.sin β/sin α.sin β])/([sin α.cos β/sin α.sin β]+[cos α.sin β/sin α.sin β])}
                  = {[cos α/sin α][cos β/sin β]-1}/{[cos β/sin β]+[cos α/sin α]}
cot (α+β) = {cot α.cot β - 1}/{cot β + cot α}
cotan (α-β) = cos(α-β)/sin (α-β)
                    = (cos α.cos β + sin α.sin β)/(sin α.cos β - cos α.sin β)
                    = {([cos α.cos β + sin α.sin β]/[sin α.cos β - cos α.sin β]) x ([1]/[sin α.sin β]/[1]/[sin α.sin β])}
                    = {([cos α.cos β/sin α.sin β]+[sin α.sin β/sin α.sin β])/([sin α.cos β/sin α.sin β]-[cos α.sin β/sin α.sin β])}
                    = {([cos α.cos β + sin α.sin β]/[sin α.sin β])/([sin α.cos β - cos α.sin β][sin α.sin β])}
                    = {[cos α/sin α][cos β/sin β]+1}/{[cos β/sin β]-[cos α/sin α]}
cot (α-β) = {cot α.cot β + 1}/{cot β - cot α}
sec (α+β) = {1} / {cos(α+β)}
                 = {1} / {cos α.cos β - sin α.sin β}
                 = {1} / {cos α.cos β([1 - sin α.sin β]/[cos α.cos β])}
                = {(1/cos α)(1/cos β)}/{1-([sinα/cosα][sinβ/cosβ])
sec (α+β) = {sec α.sec β}/{1-tanα.tanβ}
sec (α-β) = sec (α+(-β))
                = {sec α.sec(-β)} / {1-tanα.tan(-β)}
 sec (α-β) = {sec α.sec β}/{1 + tanα.tanβ}
cosec (α+β) = {1}/ {sin(α+β)}
                    = {1} / {sin α.cos β + cos α.sin β}
                    = {1} / {sin α.sin β([cos β/sin β]+[cos α/sin α])}
                    = {(1/sin α)(1/sin β)} / {cot β + cot α}
cosec (α+β) = {cosec α.cosec β}/{cotan α+cotan β}
cosec (α-β) = cosec (α+(-β))
                   = {cosec α.cosec(-β)} / {cotan α.cotan(-β)}
                   = {-cosec α.cosec β} / {cotan α - cotan β}
cosec (α-β) = {cosec β.cosec α} / {cotan β - cotan α}.