Question

prove that tan theta upon 1 minus cot theta + cot theta upon 1 minus tan theta equal to 1 + sec theta cos theta​

Answer 1

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Step-by-step explanation:

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Answer 2

Step-by-step explanation:

Answer

1−cotθ

tanθ

+

1−tanθ

cotθ

=

1−

tanθ

1

tanθ

+

1−tanθ

tanθ

1

=

tanθ−1

tan

2

θ

−

tanθ−1

tanθ

1

=

tanθ−1

tan

2

θ−

tanθ

1

=

tanθ(tanθ−1)

tan

3

θ−1

=

tanθ(tanθ−1)

(tanθ−1)(tan

2

θ+tanθ+1)

=

tanθ

tan

2

θ+tanθ+1

=tanθ+1+cotθ

=

cosθ

sinθ

+

sinθ

cosθ

+1

=1+

cosθ⋅sinθ

sin

2

θ+cos

2

θ

=1+

cosθsinθ

1

=1+secθ⋅cosecθ.