31. Simplify:
sin³Φ+cos³Φ
------------------- + (sinΦ+cosΦ)
sinΦ - cos Φ)
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MATH ALGEBRA 2 TRIGONOMETRY ALEGEBRA HOMEWORK MATH HELP
Sophia D. asked • 04/29/16
Simplify the following expression:
(cot2 theta + 1) (tan theta)
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Dennis D. answered • 04/29/16
TUTOR New to Wyzant
Graduated from UCSD, BS in Structural Engineering
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in my work, I used Φ instead of θ, but its just a variable
Trig Identities
cotΦ = cosΦ/sinΦ , tanΦ = sinΦ/cosΦ
cos2Φ + sin2Φ = 1, 2sinΦcosΦ = sinΦ =>
sinΦcosΦ = 1/2 (sin(2Φ)
1/sinΦ = cscΦ
cot2Φ = cos2Φ/sin2Φ
(cot2(theta) + 1) (tan theta)
=(cos2Φ/sin2Φ + 1 )(sinΦ/cosΦ) [multiple the tanΦ through]
=cosΦ/sinΦ + sinΦ/cosΦ [find common base, then add]
=cos2Φ + sin2Φ/ (sinΦcosΦ) [substitute with trig. identities]
= 1/(1/2 sin(2Φ)
= 2csc(2Φ)