Prove that (sinA + cosec A)2 + (cosA + secA)2 = 7 + tan’A+ cot?A
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Answer:
(sinA+cscA)
2
+(cosA+secA)
2
=sin
2
A+csc
2
A+2sinAcscA+cos
2
A+sec
2
A+2cosAsecA .......As[a²+b²+2ab=(a+b)²]
=sin
2
A+csc
2
A+2sinA×
sinA
1
+cos
2
A+sec
2
A+2cosA
cosA
1
.
........... since secA=
cosA
1
and cscA=
sinA
1
=sin
2
A+csc
2
A+2+cos
2
A+sec
2
A+2
=(sin
2
A+cos
2
A)+csc
2
A+sec
2
A+4
=1+1+cot
2
A+1+tan
2
A+4 ........... since csc
2
A=1+cot
2
A and sec
2
A=1+tan
2
A
=7+tan
2
A+cot
2
A
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