Question

2
1 + tan-A
1 – tan A
FI-
=tanA
(x)
1 + cotA
– cot A

Answer 1

Answer:

tan A/1-cot A + cot A/1-tan A = 1+ tan A + cot A?

Step-by-step explanation:

tanA/1-cotA=(sinA/cosA)/1-(cosA/sinA)

=Sin^2A/(sinA-cosA)*cosA…(1)

CotA/1-tanA=(cosA/sinA)/1-(sinA/cosA)

=cos^2A)/(cosA-sinA)*sinA….(2)

Adding equations (1) and (2)

tanA/1-cotA+cotA/1-tanA=

(sin^2A/cosA-cos^2A/sinA)*1/(sinA-cosA)

=(sin^3A-cos^3A/sinA cosA)*1/(sinA-cosA)

=(Sin^3A-cos^3A)/(sinA-cosA)*sinAcosA

We know that a^3-b^3/a-b=a^2+a*b+b^2

=Sin^2A+sinAcosA+cos^2A/sinAcosA

=tanA+1+cotA