Question

prove that cotA-cosA/CotA+CosA=sec^2A+tan^A-2secA.TanA​

Answer 1

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Answer 2

cotA-cosA/CotA+CosA=sec²A+tan²A-2secAtanA​

To prove:

cotA-cosA/CotA+CosA=sec²A+tan²A-2secAtanA​

Solution:

LHS = cotA- cosA/cotA=cosA

= 1/tanA-1/secA / 1/tanA-1/secA

=secA-tanA/secAtanA / secA+tanA/secAtanA

=secA-tanA/secA+tanA × secA-tanA/secA-tanA

=(secA-tanA)²/sec²A-tan²A

We know that

sec²A-tan²A=1

And,

(secA-tanA)² = sec²A+tan²A-2secAtanA

hence,

L.H.S=R.H.S