(1+tanA)² + (1+cotA)² = (secA+cosecA)²
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Step-by-step explanation:
To prove : (1+tanA)² + (1+cotA)² = (secA+cosecA)²
take LHS
= (1+tanA)² + (1+cotA)²
= 1+2tanA+tan²A + 1 + 2cotA + cot²A
= sec²A-tan²A+tan²A+cosec²A-cot²A+cot²A + 2(tanA+cotA)
= sec²A+cosec²A+2( (sinA/cosA) + (cosA/sinA) )
= sec²A+cosec²A+2( sin²A+cos²A)/ (sinA.cosA)
= sec²A+cosec²A+2( 1/ sinA).(1/cosA)
= sec²A+cosec²A+2secA.cosecA
= (secA+cosecA)²
= RHS
=> LHS = RHS
Hence proved
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Answer:
see the photo just solved now
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