Answer:
See explanation
Step-by-step explanation:
Simplify left and right parts separately.
<u>Left part:</u>
![\left(1+\dfrac{1}{\tan^2A}\right)\left(1+\dfrac{1}{\cot ^2A}\right)\\ \\=\left(1+\dfrac{1}{\frac{\sin^2A}{\cos^2A}}\right)\left(1+\dfrac{1}{\frac{\cos^2A}{\sin^2A}}\right)\\ \\=\left(1+\dfrac{\cos^2A}{\sin^2A}\right)\left(1+\dfrac{\sin^2A}{\cos^2A}\right)\\ \\=\dfrac{\sin^2A+\cos^2A}{\sin^2A}\cdot \dfrac{\cos^2A+\sin^A}{\cos^2A}\\ \\=\dfrac{1}{\sin^2A}\cdot \dfrac{1}{\cos^2A}\\ \\=\dfrac{1}{\sin^2A\cos^2A}](https://tex.z-dn.net/?f=%5Cleft%281%2B%5Cdfrac%7B1%7D%7B%5Ctan%5E2A%7D%5Cright%29%5Cleft%281%2B%5Cdfrac%7B1%7D%7B%5Ccot%20%5E2A%7D%5Cright%29%5C%5C%20%5C%5C%3D%5Cleft%281%2B%5Cdfrac%7B1%7D%7B%5Cfrac%7B%5Csin%5E2A%7D%7B%5Ccos%5E2A%7D%7D%5Cright%29%5Cleft%281%2B%5Cdfrac%7B1%7D%7B%5Cfrac%7B%5Ccos%5E2A%7D%7B%5Csin%5E2A%7D%7D%5Cright%29%5C%5C%20%5C%5C%3D%5Cleft%281%2B%5Cdfrac%7B%5Ccos%5E2A%7D%7B%5Csin%5E2A%7D%5Cright%29%5Cleft%281%2B%5Cdfrac%7B%5Csin%5E2A%7D%7B%5Ccos%5E2A%7D%5Cright%29%5C%5C%20%5C%5C%3D%5Cdfrac%7B%5Csin%5E2A%2B%5Ccos%5E2A%7D%7B%5Csin%5E2A%7D%5Ccdot%20%5Cdfrac%7B%5Ccos%5E2A%2B%5Csin%5EA%7D%7B%5Ccos%5E2A%7D%5C%5C%20%5C%5C%3D%5Cdfrac%7B1%7D%7B%5Csin%5E2A%7D%5Ccdot%20%5Cdfrac%7B1%7D%7B%5Ccos%5E2A%7D%5C%5C%20%5C%5C%3D%5Cdfrac%7B1%7D%7B%5Csin%5E2A%5Ccos%5E2A%7D)
<u>Right part:</u>
![\dfrac{1}{\sin^2A-\sin^4A}\\ \\=\dfrac{1}{\sin^2A(1-\sin^2A)}\\ \\=\dfrac{1}{\sin^2A\cos^2A}](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B%5Csin%5E2A-%5Csin%5E4A%7D%5C%5C%20%5C%5C%3D%5Cdfrac%7B1%7D%7B%5Csin%5E2A%281-%5Csin%5E2A%29%7D%5C%5C%20%5C%5C%3D%5Cdfrac%7B1%7D%7B%5Csin%5E2A%5Ccos%5E2A%7D)
Since simplified left and right parts are the same, then the equality is true.
Step-by-step explanation:
A mixed number consists of an integer and a proper fraction:
![a\frac{b}{c}](https://tex.z-dn.net/?f=a%5Cfrac%7Bb%7D%7Bc%7D)
where the numerator is less than the denominator (b < c).
A terminating decimal is a decimal that ends. For example, 1/2 = 0.5.
A repeating decimal is a decimal that repeats forever. For example, 1/3 = 0.33333...
You must use 2, 3, and 4 exactly once. Try different combinations and see which ones result in a terminating decimal, and which one results in a repeating decimal.