Question

Prove that :(1-tan^2A) + (1-cot^2A) =(secA- cosecA)^2​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Step-by-step explanation:

How do I prove that [math](1+\tan A)^2+(1+\cot A)^2=(\sec A+\mathrm{cosec}\,A)^2[/math]

Let A =45

Then LHS

(1+1)^2+(1+1)^2= 2^2 +2^2= 4 + 4=8

RHS

(Root 2 + Root 2)^2= (2Root2)^2=8

LHS=RHS

OR

LHS

Open Squares

(1 + tan^2A + 2 tan A) + (1+cot^2+2cotA)

1+tan^2A = Sec^2A & 1+ cot^2A = cosec^2 A

Put & Get

Sec^2 A + Cosec^2 A + 2 (tan A + Cot A)

Tan=sin/cos Cot=cos /sin

So, tan A + Cot A= (sin^2 A + Cos ^2 A)/ sin A Cos A

1/ SinA Cos A= Cosec A Sec A

LHS= Sec^2 A + Cosec^2 A + 2 Cosec A Sec A

Open RHS AND you'll get the Same hope it helps please mark as brainlliest