Question

Prove that (tanθ+sinθ) / (tanθ−sinθ) = (secθ+1) / (secθ−1)

Answer 1

Step-by-step explanation:

tan theta convert into sin theta/ cos theta

then rationalization.

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Answer 2

ANSWER

tanθ−sinθ

tanθ+sinθ

=

secθ−1

secθ+1

L.H.S=

tanθ−sinθ

tanθ+sinθ

=

cosθ

sinθ

−

1

sinθ

cosθ

sinθ

+

1

sinθ

=

cosθ

sinθ−sinθ.cosθ

cosθ

sinθ+sinθ.cosθ

=

sinθ−sinθ.cosθ

sinθ+sinθ.cosθ

=

sinθ(1−cosθ)

sinθ(1+cosθ)

=

1−

secθ

1

1+

secθ

1

=

secθ−1

secθ+1

L.H.S=R.H.SProved.

R.H.S=

tanθ−sinθ

tanθ+sinθ

=

sinθ(

sinθ

tanθ

−1)

sinθ(

sinθ

tanθ

+1)

=

cosθ.sinθ

sinθ

−1

cosθ.sinθ

sinθ

+1

=

cosθ

1

−1

cosθ

1

+1

=

secθ−1

secθ+1

L.H.S=R.H.Sproved.

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