Question

prove that sec theta+tan theta-1 / tan theta-sec theta+1 = 1+sin theta / cos theta​

Answer 1

Answer:

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Answer 2

Answer:

To Prove:

tanθ−secθ+1tanθ+secθ−1=cosθ1+sinθ

Solution:

L.H.S =tanθ−secθ+1tanθ+secθ−1

We can write, sec2θ−tan2θ=1

=tanθ−secθ+1tanθ+secθ−(sec2θ−tan2θ)

=tanθ−secθ+1tanθ+secθ−(secθ−tanθ)(secθ+tanθ)

=tanθ−secθ+1(tanθ+secθ){1−(secθ−tanθ)}

=tanθ−secθ+1(tanθ+secθ){1−secθ+tanθ}

=tanθ+secθ

=cosθsinθ+cosθ1

=cosθ1+sinθ