4 Show that sin a+B)sin(α+β)sin(α-β)4. Show that-3, given that tan

1.	4 Show that sin a+B)sin(α+β)sin(α-β)4. Show that-3, given that tan α2 tan β
Answer» sin(A+B)/sin(A-B) (sinA.cosB + cosA.sinB)/(sinA.cosB - cosA.sinB) now divide above and below by cosA.sinB, (tanA.cotB + 1)/(tanA.cotB - 1) now substitute for tanA = 2tanB, (2tanB.cotB + 1)/(2tanB.cotB - 1) (2 + 1)/(2 - 1) (using cotB = 1/tanB) =3

4 Show that sin a+B)sin(α+β)sin(α-β)4. Show that-3, given that tan α2 tan β

Answer»

sin(A+B)/sin(A-B)

(sinA.cosB + cosA.sinB)/(sinA.cosB - cosA.sinB)

now divide above and below by cosA.sinB,

(tanA.cotB + 1)/(tanA.cotB - 1)

now substitute for tanA = 2tanB,

(2tanB.cotB + 1)/(2tanB.cotB - 1)

(2 + 1)/(2 - 1) (using cotB = 1/tanB)