Question

(Sin A + Cosec A)2 + ( Cos A + Sec)2​

Answer 1

Step-by-step explanation:

(sinA+cscA)

2

+(cosA+secA)

2

=sin

2

A+csc

2

A+2sinAcscA+cos

2

A+sec

2

A+2cosAsecA .......As[a²+b²+2ab=(a+b)²]

=sin

2

A+csc

2

A+2sinA×

sinA

1

+cos

2

A+sec

2

A+2cosA

cosA

1

.

........... since secA=

cosA

1

and cscA=

sinA

1

=sin

2

A+csc

2

A+2+cos

2

A+sec

2

A+2

=(sin

2

A+cos

2

A)+csc

2

A+sec

2

A+4

=1+1+cot

2

A+1+tan

2

A+4 ........... since csc

2

A=1+cot

2

A and sec

2

A=1+tan

2

A

=7+tan

2

A+cot

2

A