Question

prove that (sinA+cosA)^2+(cosA+secA)^2 = 7+tan^2A +cot^2 A

Answer 1

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Answer 2

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solution;

l.h.s

=(sinA+cosecA)²+(cosA+secA)²

=sin²A+cosec²A+2sinAcosecA+cos²A+sec²A+2cosAsecA

=sin²A+cos²A+cosec²A+sec²A+2sinA×1/sinA+2cosA×1/cosA

=1+cosec²A+sec²A+2+2

=5+(1+cot²A)+(1+tan²A)

=7+tan²A+cot²A proved

formula used

1+tan²A=sec²A

1+cot²A=cosec²A

sin²A+cos²A=1

cosecA=1/sinA

secA=1/cosA