Question

If $S_n=co{s}^n\theta +si{n}^n\theta$, then the value of $3S_4-2S_6$ is given by

• A. 4
• B. 0
• C. 1
• D. 7

Answer 1

The correct option is C

1

Given,

$S_n=co{s}^n\theta +si{n}^n\theta \therefore 3S_4-2S_6=3(co{s}^4\theta +si{n}^4\theta )-2(co{s}^6\theta +si{n}^6\theta )=3[{(co{s}^2\theta +si{n}^2\theta )}^2-2si{n}^2\theta co{s}^2\theta ]-2\left[(co{s}^2\theta +si{n}^2\theta )(co{s}^4\theta +si{n}^4\theta -co{s}^2\theta si{n}^2\theta )\right]=3[1-2si{n}^2\theta co{s}^2\theta ]-2[{(co{s}^2\theta +si{n}^2\theta )}^2-3co{s}^2\theta si{n}^2\theta ]=3-6si{n}^2\theta co{s}^2\theta -2+6co{s}^2\theta si{n}^2\theta =1$