Is (cot^2(B)-cos^2(B))/(csc^2(B)-1)=cos^2(B) ?

The answer to whether (cot^2(B)-cos^2(B))/(csc^2(B)-1)=cos^2(B) is True

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prove (cot^2(B)-cos^2(B))/(csc^2(B)-1)=cos^2(B)

prove

\frac{cot ^{2} ( B ) - cos ^{2} ( B )}{csc ^{2} ( B ) - 1} = cos^{2} (B)

True

Solution steps

\frac{cot ^{2} ( B ) - cos ^{2} ( B )}{csc ^{2} ( B ) - 1} = cos^{2} (B)

Manipulating left side

\frac{cot ^{2} ( B ) - cos ^{2} ( B )}{csc ^{2} ( B ) - 1}

Express with sin, cos

= cos^{2} (B)

We showed that the two sides could take the same form

\Rightarrow True

cos (2 a) = 1 - 2 sin^{2} (a)

sec^{2} (x) - tan^{2} (x) = tan (x) cot (x)

\frac{tan ( θ )}{tan ( θ ) - 1} = \frac{1}{1 - cot ( θ )}

\frac{tan ^{2} ( x )}{sec ( x ) - 1} = sec (x) + 1

2 cos (x) tan (x) csc (x) = 2

Is (cot^2(B)-cos^2(B))/(csc^2(B)-1)=cos^2(B) ?
The answer to whether (cot^2(B)-cos^2(B))/(csc^2(B)-1)=cos^2(B) is True