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Question

If mn=tanAtanB , find the value of m+nm−n

A

tan (A+B)

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B

tan (A-B)

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C

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D

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Solution

The correct option is C m+nm−n=tanA+tanBtanA−tanB This is I definitely not equal to tan (A+B) or tan (A-B). Other two options are in terms of sin (A± B) or cos (A± B) We know the terms in sin (A± B) and cos (A ± B) are sinA, cosA, cosA and cosB. So we will convert tanA into sinAcosA and tanB to sinBcosB ⇒ m+nm−n = sinAcosB+sinBcosAsinAcosB−sinBcosA = sin(A+B)sin(A−B) Key steps/concepts: (1) tanA = sinAcosA (2) Formula of sin (A±B)

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