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If Cos(A+Y)/Cos(A-Y)=Cos2B , then prove that tan 2 B=(tanA)(tanY)

If Cos(A+Y)/Cos(A-Y)=Cos2B , then prove that tan2B=(tanA)(tanY)

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1 Answers

siddharth gupta
28 Points
9 years ago
COS(A+Y)/COS(A-Y)=(COS(A)COS(Y)-SIN(A)SIN(Y))/(COS(A)COS(Y)+SIN(A)SIN(Y))
DIVIDE NUMERATOR AND DENOMINATOR IN THE ABOVE EQN BY COS(A)COS(B)
ON DIVIDING THE ABOVE EQN BECOMES
(1-TAN(A)TAN(Y))/(1+TAN(A)TAN(Y))=COS(2B)=(1-TAN2(B))/(1+TAN2(B))
NOW YOU MAY EITHER CROSS MULTIPLY OR ON DIRECT OBSERVATION OF ABOVE EQN WE CAN SAY
TAN2B=TAN(A)TAN(Y)
WITH REGARDS 
SIDDHARTH GUPTA

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