What is the general solution for (csc(a)+1)(csc(a)+1)=cot^2(a) ?

The general solution for (csc(a)+1)(csc(a)+1)=cot^2(a) is a=2pin+(3pi)/2

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

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

a = 2 πn + \frac{3 π}{2}

Solution steps

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

Subtract

cot^{2} (a)

from both sides

(csc (a) + 1)^{2} - cot^{2} (a) = 0

Factor

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

(csc (a) + 1 + cot (a)) (csc (a) + 1 - cot (a)) = 0

Solving each part separately

csc (a) + 1 + cot (a) = 0 or csc (a) + 1 - cot (a) = 0

csc (a) + 1 + cot (a) = 0 : a = 2 πn + \frac{3 π}{2}

csc (a) + 1 - cot (a) = 0 : a = 2 πn + \frac{3 π}{2}

Combine all the solutions

a = 2 πn + \frac{3 π}{2}

43 sec (θ) + 7 = - 1

tan (θ) = m

4 sin^{3} (θ) = 3 sin (θ)

- 8 cos^{2} (θ) + 2 cos (θ) = - 1

cos (2 x) = 1 - 3 cos (x)

What is the general solution for (csc(a)+1)(csc(a)+1)=cot^2(a) ?
The general solution for (csc(a)+1)(csc(a)+1)=cot^2(a) is a=2pin+(3pi)/2