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`         Cos (alpha-3theta)÷cos3 theta=sin (alpha- 3theta)÷sin3theta = m then what is cos2alpha? `
5 months 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 get1= 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 writecosalpha*cos3theta + sinalpha*sin3theta= mcos3 thetaand sinalpha*cos3theta – sin3theta*cosalpha= msin3thetafrom these two eqns, eliminate sinalpha to obtain the value of cosalpha in terms of theta.after simplifying, you obtaincosalpha= m(1+3cos4theta)/4.......(2)from (1) and (2), eliminate cos4theta to obtain the answer.kindly approve :)
```
5 months ago
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