Prove 1+cot^2/1+tan^2=(1+tan/1+cot)^2
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Step-by-step explanation:
From LHS
1+cot²A/1+tan²A
=(1+cos²A/sin²A)/(1+sin²A/cos²A)
=(sin²A+cos²A/sin²A)÷(cos²A+sin²A/cos²A)
=1/sin²A÷1/cos²A
=1/sin²A×cos²A/1
=cot²A
Now,from RHS
(1+cotA/1+tanA)²
=(1+CosA/SinA÷1+SinA/CosA)²
=(SinA+cosA/sinA÷cosA+sinA/cosA)²
=(sinA+cosA)²/sin²A÷(cosA+sinA)²/cos²A
=(sinA+cosA)²/sin²A×cos²A/(sin²A+cos²A)
=cos²A/sin²A
=cot²A
therefore LHS=RHS
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