Question

what is the value of cot square 72-cosec square 72​

Answer 1

Answer:

cot square 72 - cosec square 72

cot square 72 -( 1 + cot square 72)

cot square 72 - 1 - cot square 72

-1

Answer 2

The value of $\cot^2 72$° - $\csc^2 72$° =  - 1

Step-by-step explanation:

We have,

$\cot^2 72$° - $\csc^2 72$°

To find, the value of $\cot^2 72$° - $\csc^2 72$° = ?

∴ $\cot^2 72$° - $\csc^2 72$°

Taking (- 1) as common, we get

= (- 1) [- $\cot^2 72$° - (- 1) $\csc^2 72$°]

= (- 1) (- $\cot^2 72$° + $\csc^2 72$°)

=  (- 1)($\csc^2 72$° - $\cot^2 72$°)

Using the trigonometric identity,

$\csc^2 A$ - $\cot^2 A$ = 1

=  (- 1) (1)

= - 1

Thus, the value of $\cot^2 72$° - $\csc^2 72$° =  - 1