Trigonometry help

kayoh

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Nov 30, 2012
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3) Find the exact value of tanπ/10 + tanπ/15 / 1- tanπ/10 tanπ15
4) prove the identity cosθ - sinθ / cosθ + sinθ = sec2θ - tan2θ
5) What is the solution to the equation cos2X + 2 = sinX for 0° ≤ X ≤ 360°
6) Determine the value of cosθ (sinθsecθ + tanθ / secθtanθ) if sinθ=
13/85 and cosθ = 84/85

i kinda found out how to do the first one i don't know if its right

tan (π/10 + π/15) =
tan ( 3π/30 + 2π/30) =
tan ( 5π/30) =
tan π/6 =
√3 / 3

can you help me with the rest of the questions please?
 
3) Find the exact value of [tan(π/10) + tan(π/15)] / [1- tan(π/10 tan(π15)]
4) prove the identity (cosθ - sinθ) / (cosθ + sinθ) = sec2θ - tan2θ
5) What is the solution to the equation cos2X + 2 = sinX for 0° ≤ X ≤ 360°
6) Determine the value of cosθ (sinθsecθ + tanθ / secθtanθ) if sinθ=
13/85 and cosθ = 84/85

i kinda found out how to do the first one i don't know if its right

tan (π/10 + π/15) =
tan ( 3π/30 + 2π/30) =
tan ( 5π/30) =
tan π/6 =
√3 / 3.................................Looks good to me

can you help me with the rest of the questions please?

Use proper grouping symbols as shown!

4) Hint: work on the right-hand-side (RHS) of the equation

Use Cos(2Θ) = cos2(Θ) - sin2(Θ)

5) use Cos(2Θ) = 1 - 2*sin2(Θ) and quadratic equation

6) First simplify the LHS by multiplying it out.
 
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