Question

prove that tan A/1-cotA+cot A/1-tanA= 1+tan A+ cot A=1+sec AcosecA
​

Answer 1

Step-by-step explanation:

1−cotA

tanA

+

1−tanA

cotA

=1+secAcscA

Taking L.H.S.-

1−cotA

tanA

+

1−tanA

cotA

=

1−(

tanA

1

)

tanA

+

1−tanA

(

tanA

1

)

=

tanA−1

tan

2

A

+

tanA(1−tanA)

1

=

tanA(1−tanA)

1−tan

3

A

=

tanA(1−tanA)

(1−tanA)(1+tanA+tan

2

A)

(∵a

3

−b

3

=(a−b)(a

2

+ab+b

2

))

=

tanA

sec

2

A+tanA

(∵1+tan

2

A=sec

2

A)

=1+

tanA

sec

2

A

=1+

cosAsinA

1

=1+secAcscA

= R.H.S.

Hence proved.