SOLUTION: establish each identity 44) 1- 1/2sin (2 theta) = sin^3 theta + cos^3 theta over sin theta + cos theta

Algebra.Com
Question 704213: establish each identity

44) 1- 1/2sin (2 theta) = sin^3 theta + cos^3 theta over sin theta + cos theta

Answer by AnlytcPhil(1807)   (Show Source): You can put this solution on YOUR website!
             

Factor the numerator on the right side as the sum of 
two cubes, using 

                    

                   

                   

Use the identity  on the 1st and 3rd terms:

                   

Use the identity  multiplied
through by  or 

                   

                   

Edwin

RELATED QUESTIONS

establish each identity A) 1 - sin theta over cos theta + cos theta over 1 - sin... (answered by lwsshak3)
establish each identity A) sec^4 theta - sec^2 theta = tan^4 theta + tan^2 theta (answered by solver91311)
establish each identity A) sin theta times cos theta over cos^2 theta - sin^2 theta... (answered by DrBeeee)
establish each identity sin^2 theta cos^2 theta = 1/8[ 1- cos(4 theta)] (answered by nshah11)
How do i establish the identity sin^3 theta - cos^3 theta/sin theta - cos theta = 1 +... (answered by dkppathak)
Establish the identity: tan^2(theta)cos^2(theta) +... (answered by mananth)
help the step by step process for this. establish the identity of sec theta over tan... (answered by jsmallt9)
Simplify each trig expression into 1 term: 1.) sin(theta)+cos(theta)cot(theta)... (answered by stanbon)
Prove the following identity : (cos^2 theta - sin^2 theta)/(cos^2 theta + sin theta cos... (answered by MathLover1)