Question

(Sin A + Sec A)^2 +(CosA + Cosec A)^2= (1+ cosec A sec A)^2

Answer 1

Step-by-step explanation:

(sinA+secA)²+(cosA+cosecA)²

=sin²A+sec²A+2sinAsecA +cos²A+cosec²A+ 2cosAcosecA

=1+(sec²A+cosec²A)+2(sinAsecA+cosAcosecA)

=1+(sin²A+cos²A/sin²Acos²A)+2(tanA+cotA)

=1+sec²Acosec²A+2/sinAcosA

=1+sec²Acosec²A+2secAcosecA

=(1+secAcosecA)²