Sin A (1 + tan A) + cos A(1 + cot A) = sec A + cosec A

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Sin A (1 + tan A) + cos A(1 + cot A) = sec A + cosec A

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Skylar 5 days 2021-09-12T17:30:32+00:00 1 Answer 0 views 0

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    2021-09-12T17:32:02+00:00

    Answer:

    taking LHS

    Sin A (1 + tan A) + cos A(1 + cot A)

    sinA+sinAtanA + cosA + cosAcotA

    we know that tanA = sinA/cosA &

    cotA = cosA/sinA

    sinA + sinA ×sinA/cosA+ cosA + cosA × cosA/sinA

    sinA + sin^2A/cosA + cosA + cos^2A/sinA

    taking LCM of sinA and cosA

    (sin^2AcosA+sin^2A sinA+sinAcos^2A + cos^2AcosA)/sinAcosA

    { sin^2A(cosA+sinA)+cos^2(sinA+cosA)/sinAcosA

    {(sin^2A+cos^2)(cosA+sinA)}/sinAcosA

    { 1(cosA+sinA)}/sinAcosA

    (sinA + cosA)/sinAcosA

    (sinA/sinAcosA) + (cosA/sinAcosA)

    1/cosA + 1/sinA

    secA + cosecA

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