# Trig/Precalc

posted by .

So I have two questions that have been puzzling me for quite some time and would really appreciate any help with either of them!

(a) There are four positive intergers a, b, c, and d such that 4cos(x)cos(2x)cos(4x)=cos(ax)+cos(bx)+cos(cx)+cos(dx) for all values of x. Find a+b+c+d.

I started this problem by trying to use the double-angle formulas to expand cos(2x) and cos(4x). This quickly seemed to become difficult as I was working with exponents and there didn't seem to be an easy way to simplify

(b) There are intergers a, b, c, and d such that tan(7.5)=sqrt(a)+sqrt(b)-sqrt(c)-sqrt(d). Find a+b+c+d.

I started this problem by using the fact that tan(x)=sin(x)/cos(x). Next I used the half-angle identities and sum-difference formulas to get a very ugly fraction that I had no idea how to solve.

Any help would be much appreciated - thank you in advance!

• Trig/Precalc -

(a) Try using the product-to-sum formula

cos(a)cos(b) = 1/2 (cos(a-b)+cos(a+b))

(b) We have

tan x/2 = (1-cosx)/sinx

tan 15 = (1-cos30)/sin30 = (1-√3/2)/(1/2) = 2-√3
sin15 = √((1-cos30)/2) = √((1-√3/2)/2) = √(2-√3)/2
sin15 = √((1+cos30)/2) = √((1+√3/2)/2) = √(2+√3)/2

Now apply that again, and note that

(√2+√6)^2 = 4(2+√3)

and I think things will fall out as you desire.

• Trig/Precalc -

Thank you so much for your help! I got both of those now!

## Similar Questions

1. ### trig

Reduce the following to the sine or cosine of one angle: (i) sin145*cos75 - cos145*sin75 (ii) cos35*cos15 - sin35*sin15 Use the formulae: sin(a+b)= sin(a) cos(b) + cos(a)sin(b) and cos(a+b)= cos(a)cos(b) - sin(a)sin)(b) (1)The quantity …
2. ### Trigonometry

There is an arbitrary triangle with angles A, B, and C and sides of lengths a, b, and c. Angle A is opposite side a. How do I get the formulas: b * cos C + c * cos B = a c * cos A + a * cos C = b a * cos B + b * cos A = c Are these …
3. ### pre-cal

Simplify the given expression........? (2sin2x)(cos6x) sin 2x and cos 6x can be expressed as a series of terms that involve sin x or cos x only, but the end result is not a simplification. sin 2x = 2 sinx cosx cos 6x = 32 cos^6 x -48
4. ### Math - Solving Trig Equations

What am I doing wrong? Equation: sin2x = 2cos2x Answers: 90 and 270 .... My Work: 2sin(x)cos(x) = 2cos(2x) sin(x) cos(x) = cos(2x) sin(x) cos(x) = 2cos^2(x) - 1 cos(x) (+/-)\sqrt{1 - cos^2(x)} = 2cos^2(x) - 1 cos^2(x)(1 - cos^2(x))
5. ### TRIG!

Posted by hayden on Monday, February 23, 2009 at 4:05pm. sin^6 x + cos^6 x=1 - (3/4)sin^2 2x work on one side only! Responses Trig please help! - Reiny, Monday, February 23, 2009 at 4:27pm LS looks like the sum of cubes sin^6 x + cos^6 …
6. ### Calc.

Differentiate. y= (cos x)^x u= cos x du= -sin x dx ln y = ln(cos x)^x ln y = x ln(cos x) (dy/dx)/(y)= ln(cos x) (dy/dx)= y ln(cos x) = (cos x)^x * (ln cos x) (dx/du)= x(cos x)^(x-1) * (-sin x) = - x sin(x)cos^(x-1)(x) (dy/dx)-(dx/du)= …
7. ### calculus

Differentiate. y= (cos x)^x u= cos x du= -sin x dx ln y = ln(cos x)^x ln y = x ln(cos x) (dy/dx)/(y)= ln(cos x) (dy/dx)= y ln(cos x) = (cos x)^x * (ln cos x) (dx/du)= x(cos x)^(x-1) * (-sin x) = - x sin(x)cos^(x-1)(x) (dy/dx)-(dx/du)= …
8. ### Precalculus

Solve Cos^2(x)+cos(x)=cos(2x). Give exact answers within the interval [0,2π) Ive got the equation down to -cos^2(x)+cos(x)+1=0 or and it can be simplified too sin^2(x)+cos(x)=0 If you could tell me where to go from either of these …
9. ### math

Determine exact value of cos(cos^-1(19 pi)). is this the cos (a+b)= cos a cos b- sina sin b?
10. ### Pre-Cal (Trig) Help?

The following relationship is known to be true for two angles A and B: cos(A)cos(B)-sin(A)sin(B)=0.957269 Express A in terms of the angle B. Work in degrees and report numeric values accurate to 2 decimal places. So I'm pretty lost …

More Similar Questions