trig
posted by stephani .
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 
Steve
While this might appear to be an exercise in halfangle or doubleangle 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
Similar Questions

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 … 
Precalculus(NEED HELP ASAP PLEASE!!)
cot(theta)= 3 pi < theta < 3pi/2 Find: sin(theta)= 1 ? 
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 … 
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 … 
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. 
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? 
Trigonometry
Prove the following identities: 1. (tan theta  sin theta)^2 + (1cos theta)^2 = (1sec theta) ^2 2. (12cos^2 theta) / sin theta cos theta = tan theta  cot theta 3. (sin theta + cos theta ) ^2 + (sin theta  cos theta ) ^2 = 2 Thank … 
Trigonometry
Prove the following identities: 1. (tan theta  sin theta)^2 + (1cos theta)^2 = (1sec theta) ^2 2. (12cos^2 theta) / sin theta cos theta = tan theta  cot theta 3. (sin theta + cos theta ) ^2 + (sin theta  cos theta ) ^2 = 2 Thank … 
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 … 
Math
Which of the following functions have a vertical asymptote for values of theta such that cos theta = 1?