Trigonometry

posted by .

Need help solving problems using the Trigonometric Identities: 8cos^4 thet=cos4theta+4cos2theta+3



I am a bit unsure how to solve it. I am aware that the first step I must take is to simplify the problem and then use the Product to Sum formula

Nasty one!
let's start on the right side.

I will work on each term to make typing easier.

recall that cos 2A = 2cos^2 A - 1

I will use x for theta

cos 4x = 2cos^2 2x - 1
= 2(cos2x)(cos2x) - 1
=2[(2cos^2 x - 1)(2cos^2 x - 1)] - 1.
=2[(4cos^4 x - 4cos^2 x + 1) – 1
=8cos^4 x – 8cos^2 x + 1


4cos 2x = 4(2cos^2 x – 1)
= 8cos^2 x – 4

Now putting it all together:
R.S.
= cos 4x + 4cos 2x + 3
= 8cos^4 x – 8cos^2 x + 1 + 8cos^2 x – 4 + 3
= 8cos^4 x
= Left Side

!!!!!!!WOW!!!!!!

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Simplifying with Trigonometry Identities

    Hi, I am a senior in High School having a really difficult time with two problems. I have to prove using the trigonometric identities that they equal each other but I am having a really hard time trying to get them to equal each other. …
  2. math

    Find an orthonormal basis for the subspace of R^3 consisting of all vectors(a, b, c) such that a+b+c = 0. The subspace is two-dimensional, so you can solve the problem by finding one vector that satisfies the equation and then by constructing …
  3. Trigonometry

    I don't understand how I'm supposed set the problem up or what theta is... Use the given function value(s), and trigonometric identities (including the cofunction identities), to find the indicated trigonometric functions. sec theta …
  4. Solving Inequalities?

    Ive been having problems with this soo... My first problem is this: Solve 2x-4(x+2)-6 < 0 Can someone help me step-by-step figure this out so i can at least finish the ones that are similiar to this one?
  5. Trig

    Find the value of the six trigonometric functions. t = 7(pi)/4 Can you show me step by step so I can see how this is solved?
  6. Trigonometry

    Solve the trigonometric equations. 1.) SIN²x(CSC²x-1) 2.) COT x SEC X 3.) COS²[(π/2)-x]/COS X (Note: These mathematical problems are somewhat tricky, but useful for students as of learning how to their fundamental identities. …
  7. Trigonometry

    Google this: 5.1 using fundamental identities Comcast Click and open the first result that appears on your search (Result= PDF Document). Textbook pages will appear and go to page 383 on problem #129. The directions will mention "Solve …
  8. Algebra 2

    I need help trying to solve trigonometric identity problems I just need help if someone could break it down step by step how to solve for: if cos of theta is -3/5 find csc of theta
  9. Calculus 2 (Differentiate & Decay Problem)

    I have two problems I need help on, can someone show and explain step by step how to do the problems?
  10. precalculus

    Which of the following would be the best first step when solving the following system using the substitution method?

More Similar Questions