Please solve the following questions:

Asked by manasd | 23rd Jul, 2015, 11:36: AM

Expert Answer:

G i v e n space t h a t space A plus B plus C equals straight pi Consider space the space given space expression comma space sin 2 straight B plus sin 2 straight C minus sin 2 straight A colon We space know space that comma sinC plus sinD equals 2 sin open parentheses fraction numerator straight C plus straight D over denominator 2 end fraction close parentheses cos open parentheses fraction numerator straight C minus straight D over denominator 2 end fraction close parentheses Therefore comma sin 2 straight B plus sin 2 straight C minus sin 2 straight A equals 2 sin open parentheses fraction numerator 2 straight B plus 2 straight C over denominator 2 end fraction close parentheses cos open parentheses fraction numerator 2 straight B minus 2 straight C over denominator 2 end fraction close parentheses minus sin 2 straight A space space space space space space open square brackets because sin 2 straight A equals 2 sinAcosA close square brackets space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 2 sin open parentheses straight B plus straight C close parentheses cos open parentheses straight B minus straight C close parentheses minus 2 sinAcosA space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 2 sin open parentheses straight pi minus straight A close parentheses cos open parentheses straight B minus straight C close parentheses minus 2 sinAcosA space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 2 sinAcos open parentheses straight B minus straight C close parentheses minus 2 sinAcosA space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 2 sinA open square brackets cos open parentheses straight B minus straight C close parentheses minus cosA close square brackets space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 2 sinA open square brackets cos open parentheses straight B minus straight C close parentheses minus cosA close square brackets Similarly comma space we space know space that comma cosD minus cosC equals 2 sin fraction numerator straight C plus straight D over denominator 2 end fraction sin fraction numerator straight C minus straight D over denominator 2 end fraction Thus comma space sin 2 straight B plus sin 2 straight C minus sin 2 straight A equals 2 sinA open square brackets 2 sin fraction numerator straight A plus straight B minus straight C over denominator 2 end fraction sin fraction numerator straight A minus straight B plus straight C over denominator 2 end fraction close square brackets space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 2 sinA open square brackets 2 sin fraction numerator straight pi minus straight C minus straight C over denominator 2 end fraction sin fraction numerator straight pi minus straight B minus straight B over denominator 2 end fraction close square brackets space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 2 sinA open square brackets 2 sin fraction numerator straight pi minus 2 straight C over denominator 2 end fraction sin fraction numerator straight pi minus 2 straight B over denominator 2 end fraction close square brackets space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 2 sinA open square brackets 2 cosCcosB close square brackets space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 4 sinAcosCcosB
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Answered by Vimala Ramamurthy | 23rd Jul, 2015, 06:43: PM