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Prove that SecA+tanA-1÷ tanA- secA+1=( cosA÷1- sinA)

Prove that SecA+tanA-1÷ tanA- secA+1=( cosA÷1- sinA)

Grade:10

1 Answers

Arun
25763 Points
3 years ago

secA + tanA - 1) / (tanA - secA + 1) = cosA / 1 - sinA

LHS =  (secA + tanA - 1) / (tanA - secA + 1)

              [secA + tanA - (sec2A - tan2A)] / (tanA - secA + 1)        .....expand 1 as {sec2A - tan2A}

              [secA + tanA - {(secA - tanA) (secA + tanA}] / (tanA - secA + 1)

              [secA + tanA - (1 - secA + tanA)] / (tanA - secA + 1)

              secA + tanA  = 1/cosA  +  sinA/cosA

                                      =  1 + sinA / cosA  = > cosA / 1-sinA............hence proved

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