(1-tanA)^2+(1-cotA)^2=(secA-cosecA)^2
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Step-by-step explanation:
Here,
LHS = (1-tanA)²+(1-cotA)²
= (1-2tanA+tan²A)+(1-2cotA+cot²A)
= sec²A-2tanA+cosec²A-2cotA
= sec²A+cosec²A-2(tanA+cotA)
= sec²A+cosec²A-(sinA/cosA + cosA/sinA)
= sec²A+cosec²A-2((sin²A+cos²A)/cosAsinA)
= sec²A+cosec²A-2(1/cosAsinA)
= sec²A+cosec²A-2secAcosecA
= (secA-cosecA) ²
= RHS
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