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Verify identities Will give BRAINLIST do not give me trash!! cot^2(x) – csc^2(x) = -1 show steps
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Verify identities Will give BRAINLIST do not give me trash!!
cot^2(x) – csc^2(x) = -1
show steps
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Mathematics
4 years
2021-08-09T19:52:40+00:00
2021-08-09T19:52:40+00:00 1 Answers
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Answer:
See proof below
Step-by-step explanation
cot^2(x) – csc^2(x) = -1
In trigonometry identity
cot^2x = cos²x/sin²x
Csc²x = 1/sin²x
Substitute into the original expression
cos²x/sin²x – 1/sin²x
Find the LCM
(Cos²x-1)/sin²x …. *
Recall that sin²x+cos²x = 1
Sin²x = 1-cos²x
-sin²x = -1+cos²x
-sin²x = cos²x-1 …. **
Substitute ** into *
(Cos²x-1)/sin²x
-sin²x/sin²x
= -1 (RHS)
Therefore cot^2(x) – csc^2(x) = -1 (Proved!)