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Prove: (secA-tanA)^2=(1-sinA)/(1+sinA)...

Prove: `(secA-tanA)^2=(1-sinA)/(1+sinA)`

Answer

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

Prove that: cotA/2-tanA/2=(cosA/2)/(sinA/2)-(sinA/2)/(cosA/2) =(cos^(2)A/2-sin^(2)A/2)/(sinA/2cosA/2) =cosA/(1/2.(2sinA/2cosA/2)) =(2cosA)/(sinA)=2cotA = RHS. Hence Proved.

Knowledge Check

  • What is the value of (1+sinA)/(1-sinA)-(1-sinA)/(1+sinA) ?

    A
    sec A - tan A
    B
    2sec A tan A
    C
    4sec A. tan A
    D
    4cosec A.cot A

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