Question

tan theta/1-cot theta + cot theta /1-tan theta = 1+ tan theta + cot theta​

Answer 1

Answer:

ANSWER

LHS

1−cotθ

tanθ

+

1−tanθ

cotθ

=

1−

tanθ

1

tanθ

+

1−tanθ

tanθ

1

=

tanθ

tanθ−1

tanθ

+

tanθ(1−tanθ)

1

=

tanθ−1

tan

2

θ

+

tanθ(1−tanθ)

1

=

tanθ−1

tan

2

θ

−

tanθ(tanθ−1)

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

tan

2

θ

+

tanθ

tanθ

+

tanθ

1

=tanθ+1+cotθ

=1+

cosθ

sinθ

+

sinθ

cosθ

=1+

sinθcosθ

sin

2

θ+cos

2

θ

=1+

sinθcosθ

1

=1+secθcosecθ = RHS