Is tan(θ/2)=csc^2(θ)-cot^2(θ) ?

The answer to whether tan(θ/2)=csc^2(θ)-cot^2(θ) is False

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prove tan(θ/2)=csc^2(θ)-cot^2(θ)

prove

tan (\frac{θ}{2}) = csc^{2} (θ) - cot^{2} (θ)

False

Solution steps

tan (\frac{θ}{2}) = csc^{2} (θ) - cot^{2} (θ)

Show that the two sides are not equal

For

tan (\frac{θ}{2}) = csc^{2} (θ) - cot^{2} (θ)

plug in

θ = 1

tan (\frac{1}{2}) = 0.54630 \dots

tan (\frac{1}{2})

Refine to a decimal form

= 0.54630 \dots

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

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

Use the Pythagorean identity:

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

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

= 1

= 1

The two sides are not equal

\Rightarrow False

4 + 4 cos (2 x) = 8 cos^{2} (x)

\frac{sec ( θ ) csc ( θ )}{2} = csc (2 θ)

\frac{cos ( x )}{cot ( x ) sin ( x )} = 1

\frac{1 + cos ( θ )}{csc ( θ )} = sin (θ) + cos (θ)

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

Is tan(θ/2)=csc^2(θ)-cot^2(θ) ?
The answer to whether tan(θ/2)=csc^2(θ)-cot^2(θ) is False