Question

(sinA+secA)^2 + (cosA+cosecA)^2 = 1 + (secA+cosecA)^2​

Answer 1

Answer:

Step-by-step explanation:

=sin^2 A + sec^2 A+ 2 sinA secA + cos ^2 A + cosec^2 A +2cosAcosecA

=(sin^2 A+cos^2 A) + sec^2 A +cosec^2 A+(2sinAsecA+2cosAcosecA)

=(sin^2 A+cos^2 A) + sec^2 A +cosec^2 A+ 2(sinA * 1/cosA + cosA * 1/sinA)

=1+ sec^2 A +cosec^2 A+ 2 [(sin^2 A + cos^2 A)/ sinA* cosA]

=1+ sec^2 A +cosec^2 A+ 2(1/sinA cosA)

=1+ sec^2 A +cosec^2 + 2cosec A secA

=1+(secA+cosecA)^2