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proove that cosA/(1- tanA) + sinA/(1- …

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proove that cosA/(1- tanA) + sinA/(1- cotA) = sinA +cosA

    • Posted by Sushant Dwivedi 6 years, 2 months ago

    CBSE > Class 10 > Mathematics
    • 4 answers

    Aadya Singh ? 6 years, 2 months ago

    Mine ..... Your solution is right ?

    1Thank You

    Sahil ??? 6 years, 2 months ago

    Your's or mine

    1Thank You

    Aadya Singh ? 6 years, 2 months ago

    LHS - CosA/(1-tanA) + sinA/(1-cotA) => cosA/cotA + sinA/tanA => cosA/cosA/sinA + sinA/sinA/cosA => cosA×sinA/cosA + sinA × cosA/sinA => sinA + cosA ( since, sinA get cancelled by sinA and cosA get cancelled by cosA) . Now, LHS = RHS. So, it's prove.

    1Thank You

    Sahil ??? 6 years, 2 months ago

    LHS=cosA/(1-tanA)+sinA/(1-cotA). =cosA/(1-sinA/cosA) +sinA/(1-cosA/sinA). =cosA/(cosA-sinA)/cosA+sinA/(sinA-cosA)/sinA. =cos^2A/(cosA-sinA)+sin^2A/(sinA-cosA). =(-1)(cos^2A)/(-1)(cosA-sinA)+sin^2A/(sinA-cosA). = -cos^2A/(sinA-cosA)+sin^2/(sinA-cosA). =(sin^2A-cos^2A)/(sinA-cosA). =(sinA+cosA)(sinA-cosA)/(sinA-cosA). =sinA+cosA.

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