maths
posted by Anonymous
If cosθ + cos^2 θ = 1,
then
sin^12 θ + 3 sin^10 θ + 3 sin^8 θ+ sin^6 θ + 2 sin^4 θ + 2 sin^2 θ – 2 =?

Steve
since sin^2 + cos^2 = 1,
sin^2 θ = cos θ
since cosθ + cos^2 θ = 1,
cosθ = ±(√51)/2
Just plug that in for sin^2 θ, and you have
((√51)/2)^6 + 3((√51)/2)^5 + 3((√51)/2)^4 + ((√51)/2)^3 + 2((√51)/2)^2 + 2((√51)/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+x1)
= ((√51)/2)^3 ((√5+1)/2)^3 + 2(x^2+x1)
But, since (√51)/2 is a root of x^2+x1 = 0 (from our original condition),
= (51)^3/64 + 2(0)
= 1
Respond to this Question
Similar Questions

Calculus  Challenge question
Our teacher gave us this problem as a challenge. Some of us have been working on it for a few days help! Prove that the largest area of any quadrilateral is obtained when opposite angles are supplementary. Wow, what a classic and nice … 
Math  Calculus
The identity below is significant because it relates 3 different kinds of products: a cross product and a dot product of 2 vectors on the left side, and the product of 2 real numbers on the right side. Prove the identity below.  a … 
Calculus AP
hi again im really need help TextBook: James Stewart:Essential Calculus, page 311. Here the problem #27: First make a substitution and then use integration by parts to evaluate the integral. Integral from sqrt(pi/2) TO sqrt(pi)of θ^3 … 
precalc help !!!!!!!
1) cscθsinθsin^2θ 2)sinθcscθ/tanθ 3)secθ/cotθ+tanθ 4)(1cosθ)(1+cosθ) 
Quantum Physics
We have a qubit in the state ψ>= √3/2 0>+ 1/2 1>, which we want to measure in the {Cos θ 0> + Sin θ 1>, Sin θ 0>  Cos θ 1>} basis. In order for the two possible outcomes to … 
Physics
We have a qubit in the state ψ>= √3/2 0>+ 1/2 1>, which we want to measure in the {Cos θ 0> + Sin θ 1>, Sin θ 0>  Cos θ 1>} basis. In order for the two possible outcomes to … 
Trigonometry
Hi. I am reposting this. Can you verify. Thanks. (cosθ) / (sinθ – 1) + (cosθ)/ (1 + sinθ) = 2tanθ (1 / cos^2θ) – (2) (1/cos^2θ) (sinθ / cosθ) + (sin^2θ / cos^2θ) = (1  sinθ) … 
Math Question
Given tan θ = 8/5 and sin θ < 0, find sin θ, cos θ, csc θ, sec θ, and cot θ. 
Calculusantiderivative
Find f. f ''(θ) = sin θ + cos θ, f(0) = 5, f '(0) = 3 My steps: f'(θ)=cosθsinθ+C When f'(0)=3, C=2, so f'(θ)=cosθsinθ2. f(θ)=sinθcosθ2x+D When f(0)=5, D=6, so f is … 
PRECALC
solve the equation 1. cos(θ) − sin(θ) = 1 2.2 cos(θ) tan(θ) + tan(θ) = 1 + 2 cos(θ) 3. sin(θ) cos(3θ) + cos(θ) sin(3θ) = 0 4. sin(2θ) cos(θ) − cos(2θ) sin(θ) …