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Cklug2520
24.06.2021 •
Mathematics
Hello! Verify the identity. Please show your work! Use trigonometric identities to verify each expression is equal. Yes this is from edge.
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Ответ:
See Below.
Step-by-step explanation:
We want to verify the identity:
Note that the left-hand side is a perfect square trinomial pattern. Namely:
If we let a = csc(x) and b = cot(x), we can factor it as such:
Let csc(x) = 1 / sin(x) and cot(x) = cos(x) / sin(x):
Combine fractions:
Square (but do not simplify yet):
Now, we can make a substitution. Let u = x / 2. So, x = 2u. Substitute:
Recall that cos(2u) = 1 - sin²(u). Hence:
Simplify:
Recall that sin(2u) = 2sin(u)cos(u). Hence:
Square:
Cancel:
Since sin(u) / cos(u) = tan(u):
We can substitute u back for x / 2:
Hence proven.
Ответ:
red sus
Step-by-step explanation:
red is the color of hatred and anger so therefor red sus.