If sinA + sinB = a and cosA - cosB = b then, what is the value of tan A-B/2 - Maths - Trigonometric Functions

Question

If sinA + sinB = a and cosA - cosB = b then, what is the value of
tan A-B/2?

Lovina Kansal · Accepted Answer

Dear studentGiven: sinA+sinB=a  
(1)and cosA-cosB=b    
(2)from eq(1), we havesinA+sinB=a⇒2sinA+B2cosA-B2=a     
(3)and from eq(2), we havecosA-cosB=b⇒2sinA+B2sinB-A2=b    
(4)Dividing eq(4) by (3), we get⇒2sinA+B2sinB-A22sinA+B2cosA-B2=ba⇒sinB-A2cosA-B2=ba⇒-sinA-B2cosA-B2=ba⇒tanA-B2=-ba

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If sinA + sinB = a and cosA - cosB = b then, what is the value of tan A-B/2?