Question

Prove that (sin A + cosec A)2 +(cos A+ sec A)2 = 7+tan2A+cot2A.

Answer 1

Step-by-step explanation:

Just use correct identities and try to simplify everything

Answer 2

1. 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