Question

(SinA+cosecA)2+(cosA+secA)2

Answer 1

Answer:

5+Cosec²A+Sec²A (or) 7+Cot²A+Tan²A

Step-by-step explanation:

(SinA+CosecA)²+(CosA+SecA)²

=Sin²A+Cosec²A+2SinACosecA+Cos²A+Sec²A+

2CosASecA

=Sin²A+Cosec²A+2×SinA×1/SinA + Cos²A+Sec²A+ 2CosA×1/CosA

Sin²A+Cosec²A+2+Cos²A+Sec²A+2

=4+Sin²A+Cos²A+Cosec²A+Sec²A

Sin²A+Cos²A=1

=4+1+Cosec²A+Sec²A

=5+Cosec²A+Sec²A

Cosec²A-Cot²A = 1

Cosec²A = 1+Cot²A.

Sec²A-Tan²A = 1

Sec²A = 1+Tan²A

Therefore,

5+Cosec²A+Sec²A

=5+ 1+Cot²A+ 1+Tan²A

=7+Cot²A+Tan²A