cos^(2)x-sin^(2)x=1-2sin^(2)x  

Answered question

2022-02-24

cos^(2)x-sin^(2)x=1-2sin^(2)x

Answer & Explanation

alenahelenash

alenahelenash

Expert2022-03-10Added 556 answers

Verify the following identity:
cos(x)2sin(x)2=12sin(x)2

Express cos(x)2 in terms of sine via the Pythagorean identity.
cos(x)2=1sin(x)2:
(1sin(x)2)sin(x)2=12sin(x)2

Evaluate 1sin(x)2sin(x)2.
1sin(x)2sin(x)2=12sin(x)2:
(12sin(x)2)=12sin(x)2

Come to a conclusion.
The left hand side and right hand side are identical:
Answer: (identity has been verified)

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