Prove that (sin A + cosec A)2 +(cos A+ sec A)2 = 7+tan2A+cot2A.
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Step-by-step explanation:
Just use correct identities and try to simplify everything
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- Taking LHS =
Step-by-step explanation:
(sinA+cosecA)2 + (cosA+secA)2
= sin2A + Cosec2A +2sinAcosecA + Cos2A + Sec2A +2cosAsecA
(a+b)2 = a2+b2+2ab
=sin2A+cos2A+Cosec2A+Sec2A +2sinA×1/sinA + 2cosA×1/cosA
(sin2A+cos2A=1) (cosecA=1/sinA,secA=1/cosA)
1 + 1 + cos2A +1 + tan2A +2 +2
(sec2A=1 + tan2A, cosec2A= 1 + cot2A)
= 7 + tan2A +cot2A
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