prove that sinA(1+tana) +cosA(1+cotA)=secA+cosecA please give me the answer ​

Question

prove that

sinA(1+tana) +cosA(1+cotA)=secA+cosecA

please give me the answer ​

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Mary 3 weeks 2021-10-01T14:36:56+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-10-01T14:38:14+00:00

    Answer:

    To prove sin A(1+ tan A)+ cos A(1 + cot A) = sec A + cosec A.

    LHS = sin A(1+ tan A)+ cos A(1 + cot A)

    = sin A + sin^2 A/ cos A + cos A + cos^2 A/ sin A

    = sin A + cos A + [sin^3 A + cos^3 A]/sin A cos A

    =[ sin^2 A cos A + cos^2 A sin A + sin^3 A + cos^3 A]/sin A cos A

    = [ sin^2 A cos A +cos^3 A + cos^2 A sin A + sin^3 A]/sin A cos A

    = [cos A (sin^2 A + cos^2 A) + sin A (sin^2 A + cos^2 A)]/sin A cos A

    = [cos A +sin A]/sin A cos A

    = (1/sin A) + (1/cos A)

    = cosec A + sec A = RHS.

    Proved.

    0
    2021-10-01T14:38:55+00:00

    Answer:

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