1+1/tan^2A * 1+1/cot^2A
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Answer:4
Step-by-step explanation:
(1+1/tan^2A) * (1+1/cot^2A)
=(tan^2A+1/tan^2A)*(cot^2A+1/cot^2A)
=[(tan^2A+1)*(cot^2A+1)] / (tan^2A/cot^2A)
= [(tan^2A+1)*(cot^2A+1)] / 1
{since tanA =1/cotA,=>tan^2A=1/cot^2A,=>tan^2A*cot^2A=1}
= tan^2A*cot^2A + tan^2A + cot^2A + 1
=1 + Sin^2A/Cos^2A + Cos^2A/Sin^2A+1 {sinA/cosA=tanA,cosA/sinA=cotA}
=2 +( Sin^2A*Cos^2A+Cos^2A*Sin^2A)/Sin^2A*Cos^2A
= 2 + (2Sin^2A*Cos^2A)/Sin^2A*Cos^2A
=2+2
=4
Hope this helps!!
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