180 is the least common multiple.
Using simpler trigonometric identities, the given identity was proven below.
<h3>
How to solve the trigonometric identity?</h3>
Remember that:

Then the identity can be rewritten as:

Now we can multiply both sides by cos⁴(x) to get:

Now we can use the identity:
sin²(x) + cos²(x) = 1

Thus, the identity was proven.
If you want to learn more about trigonometric identities:
brainly.com/question/7331447
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Answer:
120960
Step-by-step explanation:
Given that a librarian has a set of ten different books, including four different books about Abraham Lincoln.
The librarian wants to put the ten books on a shelf with the four Lincoln books next to each other, somewhere on the shelf among the other six different books.
First arrnage the 6 other books in the shelf.
This can be done in 
Now arrange the 4 books of Lincoln
This can be done in 
Now we have 7 places to insert Lincoln books including two corners and in between.
Thus this can be done in 7 ways
Total no of ways = 
2 7/12 hours
X=101/2 - ( 3+4+1/4+2/3)
X=101/2 - 7 + (1/4+2/3)
1/4+2/3= 11/12
101/2 - 7 =3 1/5
X = 3 1/5 - 11/12 = 2 7/12