Tuesday

September 2, 2014

September 2, 2014

Posted by **Anonymous** on Friday, January 11, 2013 at 10:49am.

then

sin^12 θ + 3 sin^10 θ + 3 sin^8 θ+ sin^6 θ + 2 sin^4 θ + 2 sin^2 θ – 2 =?

- maths -
**Steve**, Friday, January 11, 2013 at 11:32amsince sin^2 + cos^2 = 1,

sin^2 θ = cos θ

since cosθ + cos^2 θ = 1,

cosθ = ±(√5-1)/2

Just plug that in for sin^2 θ, and you have

((√5-1)/2)^6 + 3((√5-1)/2)^5 + 3((√5-1)/2)^4 + ((√5-1)/2)^3 + 2((√5-1)/2)^2 + 2((√5-1)/2) - 2

= 1

Thank you wolframalpha!

Now, how can we get that for ourselves?

If you let x = sin^2 θ, the above is

x^3 (x+1)^3 + 2(x^2+x-1)

= ((√5-1)/2)^3 ((√5+1)/2)^3 + 2(x^2+x-1)

But, since (√5-1)/2 is a root of x^2+x-1 = 0 (from our original condition),

= (5-1)^3/64 + 2(0)

= 1

**Answer this Question**

**Related Questions**

Math - Calculus - The identity below is significant because it relates 3 ...

Algebra 2/ Trigonometry - The expression oos˛ θ/sin θ + sin θ is ...

Trigonometry - Hi. I am reposting this. Can you verify. Thanks. (cosθ) / (...

Calculus - A vehicle moves along a straight path with a speed of 4m/s. A ...

Calculus - Challenge question - Our teacher gave us this problem as a challenge...

pre-calc help !!!!!!! - 1) cscθsinθ-sin^2θ 2)sinθcscθ/...

Physics - We have a qubit in the state |ψ>= √3/2 |0>+ 1/2 |1>...

Calculus AP - hi again im really need help TextBook: James Stewart:Essential ...

Trigonometry - Which of the following is equivalent to 1 − cos 2 θ/...

Quantum Physics - We have a qubit in the state |ψ>= √3/2 |0>+ 1...