trig

posted by .

Hi there! I NEED SERIOUS HELP, PLEASE!!! i have such a hard time with verifying identities! The question is:

[(sin(theta/2)) / csc(theta/2)] + [(cos (theta/2) / sec(theta/2)] = 1

I have a few ideas on how to solve this, but am mainly not sure how to get rid of (theta/2). I am taking trig online and use professor notes and the textbook, in addition to google searches.

I would normally try to add both fractions if they both had the same denominator, but am unsure how to find a common denominator in this question. Do I even need to be finding a common denominator??



If I am shown how to get rid of (theta/2) to make "2sin theta", or somehow "sin^2 theta", I would then do [(1/csc theta) / (1/sin theta)] + [(1/sec theta) / (1/cos theta)] .... which even then, I am not sure if that will get me anywhere.

OR

Do I cross multiply numerators together and denominators together?? Making it
[(sin(theta/2)cos(theta/2)] / [(csc(theta/2)sec(theta/2)] ?

***I would mainly appreciate a formula to mimic, and any form of help is GREATLY appreciated it. Thank you for your time and help in advance!

Stephani

  • trig -

    While this might appear to be an exercise in half-angle or double-angle formulas, it is really just a check to see whether you remember your basic trig definitions:

    cscθ = 1/sinθ and secθ = 1/cosθ
    You happen to be using θ/2, but the principle holds.
    so, since cscθ=1/sinθ, 1/cscθ = sinθ

    [(sin(θ/2)) / csc(θ/2)] + [(cos (θ/2) / sec(θ/2)] = 1
    [sin(θ/2) * sin(θ/2)] + cos(θ/2) * cos(θ/2)] = 1
    sin^2(θ/2) + cos^2(θ/2) = 1
    as we all know, this is true.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Calculus

    I wanted to confirm that I solved these problems correctly (we had to convert the polar curves to Cartesian equations). 1.rcos(theta)=1 x=1 2.r=2*sin(theta)+2*cos(theta) r^2=2rsin(theta)+2rcos(theta) x^2+y^2=2y+2x (a little unsure …
  2. Precalculus(NEED HELP ASAP PLEASE!!)

    cot(theta)= 3 pi < theta < 3pi/2 Find: sin(theta)= -1 ?
  3. Precalculus check answers help!

    1.) Find an expression equivalent to sec theta sin theta cot theta csc theta. tan theta csc theta sec theta ~ sin theta 2.) Find an expression equivalent to cos theta/sin theta . tan theta cot theta ~ sec theta csc theta 3.) Simplify …
  4. Precalculus check answers help!

    1.) Find an expression equivalent to sec theta sin theta cot theta csc theta. tan theta csc theta sec theta ~ sin theta 2.) Find an expression equivalent to cos theta/sin theta . tan theta cot theta ~ sec theta csc theta 3.) Simplify …
  5. trig

    If sin theta is equal to 5/13 and theta is an angle in quadrant II find the value of cos theta, sec theta, tan theta, csc theta, cot theta.
  6. math

    I have a question I have been working on since yesterday and I am not making this up. I couldn't get the right answer. If sin theta = -2/3, which of the following are possible?
  7. Trigonometry

    Prove the following identities: 1. (tan theta - sin theta)^2 + (1-cos theta)^2 = (1-sec theta) ^2 2. (1-2cos^2 theta) / sin theta cos theta = tan theta - cot theta 3. (sin theta + cos theta ) ^2 + (sin theta - cos theta ) ^2 = 2 Thank …
  8. Trigonometry

    Prove the following identities: 1. (tan theta - sin theta)^2 + (1-cos theta)^2 = (1-sec theta) ^2 2. (1-2cos^2 theta) / sin theta cos theta = tan theta - cot theta 3. (sin theta + cos theta ) ^2 + (sin theta - cos theta ) ^2 = 2 Thank …
  9. Precalculus

    Circle O below has radius 1. Eight segment lengths are labeled with lowercase letters. Six of these equal a trigonometric function of theta. Your answer to this problem should be a six letter sequence whose letters represent the segment …
  10. Math

    Which of the following functions have a vertical asymptote for values of theta such that cos theta = 1?

More Similar Questions