cot
4
A+cot
2
A is equal to:
- Acosec
4
A+cosec
2
A - Bcosec
4
A−cosec
2
A - Ccosec
2
A−cosec
4
A - Dcosec
4
A−cosecA
Solution & Step-by-step Explanation
Let's simplify the given expression:
E=cot
4
A+cot
2
A
Factor out cot
2
A:
E=cot
2
A(cot
2
A+1)
We know from standard trigonometric identities that:
cot
2
A+1=cosec
2
A
And, cot
2
A=cosec
2
A−1.
Substitute these identities back into the factored expression:
E=(cosec
2
A−1)(cosec
2
A)
E=cosec
4
A−cosec
2
A
Therefore, cot
4
A+cot
2
A=cosec
4
A−cosec
2
A.
E=cot
4
A+cot
2
A
Factor out cot
2
A:
E=cot
2
A(cot
2
A+1)
We know from standard trigonometric identities that:
cot
2
A+1=cosec
2
A
And, cot
2
A=cosec
2
A−1.
Substitute these identities back into the factored expression:
E=(cosec
2
A−1)(cosec
2
A)
E=cosec
4
A−cosec
2
A
Therefore, cot
4
A+cot
2
A=cosec
4
A−cosec
2
A.