Question

Prove that (cosec theta - sin theta)(sec theta - cos theta)=1/tan theta + cot theta

Answer 1

Let  theta be represented by A.

LHS = (1/sinA  - sinA) (1/cos A  - cos A)
        = (1 - sin² A) /sinA   *  (1 - cos² A) / cos A
        = cos A sin A        after simplification
        = cos² A * tan A
        = Tan A / sec² A
        = Tan A / (1 + tan² A)
        = 1 / [ 1/tan A  + tan A)
        = 1 / [ cot A + tan A]

Answer 2

Answer:

Guys plz mark as excellent so the slontion is:

Step-by-step explanation:

1st let us consider theta be A

LHS= (1/sinA-sinA) (1/cosA-cosA)

      = (1-sin2A/sinA) (1-cos2A/cosA)

      = (cos2A/sinA) (sin2A/cosA)

      = sinA.cosA

RHS= 1/tanA+cotA

      = 1/sinA/cosA+cosA/sinA

      = 1/sin2A+cos2A/sinA.cosA

      = sinA.cosA/sin2A+cos2A  

          Reason:{sin2A+cos2A= 1}

      = sinA.cosA

Hence LHS=RHS= sinA.cosA

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