# Compound angles

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Question

# The value of sin2 12° + sin2 21° + sin2 39° + sin2 48° - sin2 9° - sin2 18° is ______ .

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Solution

## ${\mathrm{sin}}^{2}{12}^{\circ }+{\mathrm{sin}}^{2}{21}^{\circ }+{\mathrm{sin}}^{2}{39}^{\circ }+{\mathrm{sin}}^{2}{48}^{\circ }-{\mathrm{sin}}^{2}{9}^{\circ }-{\mathrm{sin}}^{2}{18}^{\circ }$$={\mathrm{sin}}^{2}{12}^{\circ }+{\mathrm{sin}}^{2}{21}^{\circ }+\left({\mathrm{sin}}^{2}{39}^{\circ }-{\mathrm{sin}}^{2}{9}^{\circ }\right)+\left({\mathrm{sin}}^{2}{48}^{\circ }-{\mathrm{sin}}^{2}{18}^{\circ }\right)$$=1-\left({\mathrm{cos}}^{2}{12}^{\circ }-{\mathrm{sin}}^{2}{21}^{\circ }\right)+\mathrm{sin}{48}^{\circ }\mathrm{sin}{30}^{\circ }+\mathrm{sin}{66}^{\circ }\mathrm{sin}{30}^{\circ }$

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In a $∆$ABC, if tan A : tan B : tan c = 3 : 4: 5, then the value of sin A . sin B . sin C is equal to