Question

(sin A+cosecA)^2+(cosA+secA)^2=7+tan^2A+cot^2A

Answer 1

It is very simple let's do it!

Proof:-
(SinA+cosecA)^2+(CosA+SecA)^2
{Identity:-(a+b)^2=a^2+b^2+2ab}

SinA^2+CosecA^2+2SinA.CosecA+CosA^2+SecA^2+2CosA.SecA
{IDENTITIES:-
SinA^2+CosA^2=1
SinA×CosecA=1 as cosecA is reciprocal of SinA
CosA×SecA=1 as SecA is reciprocal of CosA
CosecA^2=1+CotA^2
SecA^2=1+TanA^2}

SinA^2+CosA^2+2SinA.CosecA+2CosA.SecA+CosecA^2+SecA^2
=1+2+2+1+CotA^2+1+TanA^2
=7+TanA^2+CotA^2
LHS=RHS
Hence proved...

Answer 2

Hope this will be helpful to you