InterviewSolution
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InterviewSolution
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If `sinalpha, sin^2alpha, 1 , sin^4alpha and sin^6alpha` are in A.P., where `-pi < alpha < pi,` then `alpha` lies in the intervalA. `(-pi//2,pi//2)`B. `(-pi//3,pi//3)`C. `(-pi//6,pi//6)`D. none of these |
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Answer» Correct Answer - D It is given that `sinalpha,sin^(2)alpha,1,sin^(4)alpha,sin^(5)alpha` are in A.P. `:." "sinalpha,sin^(2)alpha,1` are also in A.P. `rArr" "2sin^(2)alpha=sinalpha+1` `2sin^(2)alpha-sinalpha-1=0` `rArr" "(2sinalpha+a)(sinalpha-1)=0` `rArr" "sinalpha=-1//2or,sinalpha=1` `rArr" "alpha=-pi//6or,alpha=pi//2" "[because-piltalphaltpi]` For `alpha=-pi//6`, the given sequence becomes `-(1)/(2),(1)/(4),1(1)/(16),-(1)/(32)`. Clearly, it is not an A.P. for `alpha=pi//2`, the given sequence becomes 1,1,1,1,1 which is an A.P. But, `alpha=pi//2` does nnot lie in any of the given intervals. |
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