Prove that : (Sin A + cosec A)2 + (cos A + sec A)2 =7 + tan2 A + cot2 A
Answers
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
Hence proved.
Step-by-step explanation:
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Answer:
7 + tan2 A + cot2 A
Step-by-step explanation:
= sin 2A + csc 2A + 2 + cos 2A + sec 2A +2
= (sin 2A + cos 2A) + csc 2A + sec 2A + 4
= 1 + 1 cot 2A + 1 + tan 2A + 4 ... since csc
= 2A = 1 + cot 2A and sec 2A = 1+ tan 2A
= 7 + tan 2 A + cot 2A