Question

(SinA + Cosec A)² +(CosA +SecA)² = 7+tan²A+ Cot²A.​

Answer 1

Step-by-step explanation:

=(sinA+cosecA)²+(cosA+secA)²

=sin²A+cosec²A+2sinAcosecA+cos²A+sec²A+2cosAsecA

=sin²A+cos²A+cosec²A+sec²A+2sinA×1/sinA+2cosA×1/cosA

=1+cosec²A+sec²A+2+2

=5+(1+cot²A)+(1+tan²A)

=7+tan²A+cot²A

Identities used:

1+tan²A=sec²A

1+cot²A=cosec²A

sin²A+cos²A=1

cosecA=1/sinA

secA=1/cosA

.......

Answer 2

Step-by-step explanation:

sinsquareA+cosecsquareA+2sinA×cosecA+cossquareA+secsquareA+2cosA×secA

sinsquareA+cossquareA+2sinAcosecA+2cosA×secA+cosecsquareA+secsquareA

1+2×1+2×1+1+cotsquareA+1+tansquareA

1+2+2+1+1+cotsquareA+tansquareA

7+tansquareA+cotsquareA