Is cot^2(-θ)+1=csc^2(θ) ?

The answer to whether cot^2(-θ)+1=csc^2(θ) is True

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prove cot^2(-θ)+1=csc^2(θ)

prove

cot^{2} (- θ) + 1 = csc^{2} (θ)

True

Solution steps

cot^{2} (- θ) + 1 = csc^{2} (θ)

Manipulating left side

cot^{2} (- θ) + 1

Use the negative angle identity:

cot (- x) = - cot (x)

= 1 + (- cot (θ))^{2}

Simplify

= 1 + cot^{2} (θ)

Rewrite using trig identities

1 + cot^{2} (θ)

Use the Pythagorean identity:

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

= csc^{2} (θ)

= csc^{2} (θ)

We showed that the two sides could take the same form

\Rightarrow True

\frac{1 - csc ^{2} ( t )}{csc ^{2} ( t )} = \frac{- 1}{sec ^{2} ( t )}

cot (θ) = cos (θ) csc (θ)

sech^{2} (x) = 1 - tanh^{2} (x)

\frac{cos ( a + b )}{cos ( a - b )} = \frac{1 - tan ( a ) tan ( b )}{1 + tan ( a ) tan ( b )}

(1 + sin (θ))^{2} + cos^{2} (θ) = 2 (1 + sin (θ))