Basic Trigometric Identities?
2007-12-03 4:55 pm
How does sin squared theta cos squared theta minus cos sqaured theta equal negative cos to the forth power theta?
回答 (3)
2007-12-03 5:03 pm
✔ 最佳答案
sin²θcos²θ - cos²θcos²θ(sin²θ - 1)
cos²θ(-cos²θ)
-cos⁴θ
2007-12-03 5:18 pm
U have to know the basic trigo identity to solve this question.
ie. cos^2 + sin^2 = 1
cos^2 = 1-sin^2
Hence,
sin^2(cos^2) - cos^2 = cos^2 ( sin^2-1), factorising out the common term,
then, using the basic trigo that was introduced previously,
cos^2 (sin^2-1) = -cos^2 (1-sin^2)
= -cos^2 (cos^2)
= -cos^4
ie. cos^2 + sin^2 = 1
cos^2 = 1-sin^2
Hence,
sin^2(cos^2) - cos^2 = cos^2 ( sin^2-1), factorising out the common term,
then, using the basic trigo that was introduced previously,
cos^2 (sin^2-1) = -cos^2 (1-sin^2)
= -cos^2 (cos^2)
= -cos^4
2007-12-03 5:03 pm
now on cos = c , sin = s
s^2 . c^2 - c^2 = c^2 (s^2 -1 ) = -c^2 ( 1-s^2) = -c^2 (c^2) = -c^4
s^2 . c^2 - c^2 = c^2 (s^2 -1 ) = -c^2 ( 1-s^2) = -c^2 (c^2) = -c^4
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