(sinA+cosecA)2+(cosA+secA)2=7+tan2A+cot2A
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=(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
Identities used:
1+tan²A=sec²A
1+cot²A=cosec²A
sin²A+cos²A=1
cosecA=1/sinA
secA=1/cosA
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