Question

How can I prove, tan A/1-cot A + cot A/1-tan A = 1+ tan A + cot A?

Answer 1

Step-by-step explanation:

[tanA/(1-cotA)]+[cotA/(1-tanA)]

=[tanA/(1–1/tanA)]+[cotA/(1-tanA)]

=[tan²Α/(tanA-1)]- [cotA/(tanA-1)]

= (tan²Α-cotA)/(tanA-1)

= [tan²A-(1/tanA)]/(tanA-1)

=( tan³Α-1)/(tanA-1)tanA

= (tanA-1)(tan²Α+1+tanA)/(tanA-1)tanA

= (tan²Α+tanA+1)/tanA

=1+tanA+cotA