Prove that- tan A/1-cot A + cot A/1-tan A=1+tan A+cot A
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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
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