What is the value of csc^2(-132)-cot^2(-132) ?

The value of csc^2(-132)-cot^2(-132) is 1

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csc^2(-132)-cot^2(-132)

csc^{2} (- 13 2^{\circ}) - cot^{2} (- 13 2^{\circ})

1

Solution steps

csc^{2} (- 13 2^{\circ}) - cot^{2} (- 13 2^{\circ})

Use the following property:

cot (- x) = - cot (x)

cot (- 13 2^{\circ}) = - cot (13 2^{\circ})

= csc^{2} (- 13 2^{\circ}) - (- cot (13 2^{\circ}))^{2}

Use the following property:

csc (- x) = - csc (x)

csc (- 13 2^{\circ}) = - csc (13 2^{\circ})

= (- csc (13 2^{\circ}))^{2} - (- cot (13 2^{\circ}))^{2}

Simplify

= csc^{2} (13 2^{\circ}) - cot^{2} (13 2^{\circ})

Rewrite using trig identities:

1

csc^{2} (13 2^{\circ}) - cot^{2} (13 2^{\circ})

Use the Pythagorean identity:

csc^{2} (x) = 1 + cot^{2} (x)

csc^{2} (x) - cot^{2} (x) = 1

= 1

= 1

- cot (3 0^{\circ})

sin (6 0^{\circ}) \cdot 3

sin (6 0^{\circ}) \cdot 8

tan (sin (\frac{8}{17}) - cos (\frac{3}{5}))

1 + 2 cos (2 π)

What is the value of csc^2(-132)-cot^2(-132) ?
The value of csc^2(-132)-cot^2(-132) is 1