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if sinA=xsin(A+2B) then show that tan(A+B)=((1+x)÷(1-x))tanB

if sinA=xsin(A+2B) then show that tan(A+B)=((1+x)÷(1-x))tanB

Grade:12th pass

1 Answers

Shashank Singh
askIITians Faculty 57 Points
3 years ago
sin(A+2B)= sinA / x
now,
sin(A+2B)+sinA= 2sin(A+2B+A)/2 cos(A+2B-A)/2
sin(A+2B)+sinA= 2sin(A+B)cos(B)
sinA / x + sinA = 2sin(A+B)cos(B)
sinA(1/x+1)= 2sin(A+B)cos(B)............ (1)

sin(A+2B)-sinA = 2sin(A+2B-A)/2 cos(A+2B+A)/2
sin A / x – sinA = 2sin(B)cos(A+B)
sinA(1/x-1) = 2sinB cos(A+B)......... (2)
by dividing (1) by (2), we get
(1+x)/(1-x)= tan(A+B)/ tanB
tan(A+B)= tanB(1+x)/(1-x)............. [ans]


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