Question

Prove that sin a + cosec a square + cos a + sec a square is equals to 7 + tan square a + cot square a

Answer 1

Solution:

LHS = (sinA+cosecA)²+(cosA+secA)²

= sin²A+cosec²A+2sinAcosecA

+cos²A+sec²A+2cosAsecA

= (sin²A+cos²A)

+cosec²A+sec²A+2+2

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since ,i) sinAcosecA=1

ii)cosAsecA=1

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= 1+1+cot²A+1+tan²A+4

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Since , i) cosec²A = 1+tan²A,

ii) sec²A = 1+tan²A

iii) sin²A + cos²A = 1

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= 7+tan²A+cot²A

= RHS

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