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Solve `(sin^3x/2-cos^3x/2)/(2+sinx)=(cosx)/3` |
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Answer» `("sin"^(3) x/2-"cos"^(3)x/2)/(2 + sin x)=(cos x)/3` or `(("sin"x/2-"cos"x/2)(1+"sin"x/2"cos"x/2))/(2(1+"sin" x/2"cos"x/2))=(cos x)/3` or `"sin"x/2-"cos"x/2=2/3 cos x` or `1-sin x=4/9 cos^(2) x` (On squaring) or `4/9 sin^(2) x-sin x+1-4/9=0` or `4 sin^(2) x-9 sin x+5=0` or `(4 sin x-5) (sin x -1)=0` or `sin x=1` `rArr x=2 npi+pi/2, n in Z` |
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