Is csc^2(θ)+1=cot^2(θ) ?

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

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prove csc^2(θ)+1=cot^2(θ)

prove

csc^{2} (θ) + 1 = cot^{2} (θ)

False

Solution steps

csc^{2} (θ) + 1 = cot^{2} (θ)

Show that the two sides are not equal

For

csc^{2} (θ) + 1 = cot^{2} (θ)

plug in

θ = 1

csc^{2} (1) + 1 = 2.41228 \dots

csc^{2} (1) + 1

Refine to a decimal form

= 2.41228 \dots

cot^{2} (1) = 0.41228 \dots

cot^{2} (1)

Refine to a decimal form

= 0.41228 \dots

The two sides are not equal

\Rightarrow False

cos (x) sin (x) = \frac{sin ( x )}{sec ( x )}

- sin^{2} (θ) = cos^{2} (θ)

sec^{2} (x) = \frac{cos ( x )}{sin ( x )}

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

1 + tan^{2} (B) = sec^{2} (B)