Is (csc(a)+1)(csc(a)-1)=cot^2(a) ?

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

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prove (csc(a)+1)(csc(a)-1)=cot^2(a)

prove

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

True

Solution steps

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

Manipulating left side

(csc (a) + 1) (csc (a) - 1)

Expand

(csc (a) + 1) (csc (a) - 1) : csc^{2} (a) - 1

= csc^{2} (a) - 1

Use the Pythagorean identity:

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

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

= cot^{2} (a)

We showed that the two sides could take the same form

\Rightarrow True

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

cos (4 θ) = cos^{2} (2 θ) - sin^{2} (2 θ)

- 30 cos (3 x) sin (3 x) = - 15 sin (6 x)

sec (b) cot (b) = csc (b)

sin (A + B) = sin (A) + sin (B)

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