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Cos (alpha-3theta)÷cos 3 theta=sin (alpha- 3theta)÷sin 3 theta = m then what is cos2alpha?

 
Cos (alpha-3theta)÷cos3 theta=sin (alpha- 3theta)÷sin3theta = m then what is cos2alpha?
 

Grade:11

1 Answers

Aditya Gupta
2081 Points
4 years ago
cos alpha value is coming out to be (2 – m^2)/m.
obviously you can find cos2alpha by using cos2alpha= 2cos^2alpha – 1 in terms of m.
to prove that cos alpha= (2 – m^2)/m, you need to note that Cos (alpha-3theta)= mcos3 theta and sin (alpha- 3theta)= msin3theta so square and add to get
1= m^2(sin^6theta + cos^6theta)= m^2(1 – 3sin^2(2theta)/4)= m^2(3cos4theta+5)/8.......(1)
now, from Cos (alpha-3theta)= mcos3 theta and sin (alpha- 3theta)= msin3theta, we can expand to write
cosalpha*cos3theta + sinalpha*sin3theta= mcos3 theta
and sinalpha*cos3theta – sin3theta*cosalpha= msin3theta
from these two eqns, eliminate sinalpha to obtain the value of cosalpha in terms of theta.
after simplifying, you obtain
cosalpha= m(1+3cos4theta)/4.......(2)
from (1) and (2), eliminate cos4theta to obtain the answer.
kindly approve :)

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