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If tanA=a
then find sin4A-2sin2A/ sin4A+2sin2A​

User Pmlarocque
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1 Answer

2 votes

Answer:

The value of the given expression is


(sin4A-2sin2A)/(sin4A+2sin2A)=-a^2

Step by step Explanation:

Given that
tanA=a

To find the value of
(sin4A-2sin2A)/(sin4A+2sin2A)

Let us find the value of the expression :


(sin4A-2sin2A)/(sin4A+2sin2A)=(2cos2Asin2A-2sin2A)/(2cos2Asin2A+2sin2A) ( by using the formula
sin2A=2cosAsinA here A=2A)


=(2sin2A(cos2A-1))/(2sin2A(cos2A+1))


=((cos2A-1))/((cos2A+1))


=((-(1-cos2A)))/((1+cos2A))(using
sin^2A+cos^2A=1 here A=2A)


=(-(sin^2A+cos^2A-(cos^2A-sin^2A)))/(sin^2A+cos^2A+(cos^2A-sin^2A))(using
cos2A=cos^2A-sin^2A here A=2A)


=(-(sin^2A+cos^2A-cos^2A+sin^2A))/(sin^2A+cos^2A+(cos^2A-sin^2A))


=(-(sin^2A+sin^2A))/(cos^2A+cos^2A)


=(-2sin^2A)/(2cos^2A)


=-(sin^2A)/(cos^2A)


=-tan^2A ( using
tanA=(sinA)/(cosA) here A=2A )


=-a^2 (since tanA=a given )

Therefore
(sin4A-2sin2A)/(sin4A+2sin2A)=-a^2

User Mark Korzhov
by
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