How do I solve this trigonometric function???

How do I prove that:

4sin^2 theta (don't know how to type it) +2cos^s theta = 4 - 2cos^2 theta

Please and Thanks.

5 Answers

Relevance
  • Anonymous
    1 decade ago
    Favorite Answer

    Come on, this is an EASY one.

    Here's how you do identities in general. Look to see what the differences are in the two sides. Then, look for an identity that can fix those differences.

    For example, the main difference between the left and right side is, there is sin^2 on the left, but not on the right. So somehow, the sin^2 has to disappear. Additionally, there are only cos^2's on the right, so whatever you do you your sin^2, it has to turn into some form of cos^2.

    Are you GETTING this?

    Start with the left side. Replace sin^2 (theta) with 1 - cos^2 (theta). Do the algebra that ensues to get the right side.

    • Commenter avatarLogin to reply the answers
  • 1 decade ago

    The equation can be written as

    4sin^2 theta + 2cos^2 theta +2cos^2 theta = 4

    4sin^2 theta + 4cos^2 theta = 4

    4( sin^2 theta + cos^2 theta) = 4

    since sin^2 theta + cos^2 theta = 1

    4(1) = 4

    4 = 4

    Its proved

    • Commenter avatarLogin to reply the answers
  • 1 decade ago

    I never liked proofs much. Basically you start applying your trig rules and equivalencies to one side of the equation until it looks like the other. You might wish to do some simplification, if possible, before you start.

    • Commenter avatarLogin to reply the answers
  • 1 decade ago

    You know that (sin θ)^2 + (cos θ)^2 = 1 for all θ.

    So rewrite your expression as

    4(sin θ)^2 + 2(cos θ)^2

    = 4(sin θ)^2 + 4(cos θ)^2 - 2(cos θ)^2

    = 4[(sin θ)^2 + (cos θ)^2] - 2(cos θ)^2

    = 4 - 2(cos θ)^2.

    • Commenter avatarLogin to reply the answers
  • How do you think about the answers? You can sign in to vote the answer.
  • Anonymous
    4 years ago

    hint: enable t = cos(x) the equation turns into t^2 +t =0 t(t +one million) =0 t =0 or t =-one million remedy cos(x) =-one million ----> x = (2n+one million)Pi (n =0, +/-one million; +/-2;......) cos(x) =0 x = pi/2 + 2kpi (ok =0, +/-one million; +/-2 ;.....)

    • Commenter avatarLogin to reply the answers
Still have questions? Get your answers by asking now.