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

Apply Difference of Two Squares Formula:

(a + b) (a - b) = a^{2} - b^{2}

a = csc (a), b = 1

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

Apply rule

1^{a} = 1

1^{2} = 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

(sec (x)) (csc (x)) = cot (x) + tan (x)

\frac{cos ( θ )}{1 + sin ( θ )} = sec (θ) - tan (θ)

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

sec^{4} (t) - tan^{4} (t) = 1 + 2 tan^{2} (t)

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

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