Trigonometric Identities : Proofs and Simplifying Trigonometric Expressions
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Please explain how to work these problems in steps
1. Prove this identity: sin(x+y)/sin(x-y) = coty+cotx/coty-cotx
8. Simplify: 2sinxcos³x-2sin³xcosx
9. If cosx=-¼and Pi/2 < x < pi, then cos (pi/6 - x) = ?
10. Prove this identity: cos8x=cos²4x-sin²4x.
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Solution Summary
Trigonometric identities are proven and simplifying trigonometric expressions is investigated and discussed. The solution is detailed and well presented.
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Please see the attached file.
NOTE: SQRT means the square root.
The following formula is used extensively:
Cos(a+b) = cos(a)cos(b) - sin(a) sin(b) (1)
Sin(a+b) = sin(a)cos(b) + cos(a)sin(b) (2)
From which can get:
cos(2a) = cos2a - sin2a (3)
sin(2a) = 2(cos a) (sin ...
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