Question

prove root secA-1 by sec+1 + root secA+1 by sec A-1= 2cosec A​

Answer 1

Step-by-step explanation:

secA−1

1

+

secA+1

1

=2cosec.cotA

LHS=

secA−1

1

+

secA+1

1

=

cosA

1

−1

1

+

cosA

1

+1

1

=

1−cosA

cosA

+

1+cosA

cosA

=cosA(

1−cos

2

A

1+cosA+1−cosA

=2cosA×

sin

2

A

1

=2×

sinA

cosA

×

sinA

1

=2cotAcosecA