prove that (sinA + cosecA)² + (cosA + secA)² = 7 + tan²A + cot²A
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(sinA+cscA)2+(cosA+secA)2
=sin2A+csc2A+2sinAcscA+cos2A+sec2A+2cosAsecA .......As[a²+b²+2ab=(a+b)²]
=sin2A+csc2A+2sinA×sinA1+cos2A+sec2A+2cosAcosA1 .
........... since secA=cosA1 and cscA=sinA1
=sin2A+csc2A+2+cos2A+sec2A+2
=(sin2A+cos2A)+csc2A+sec2A+4
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