Points-D-E-are-taken-on-the-side-BC-of-a-ABC-such-that-BD-DE-EC-If-BAD-x-DAE-y-EAC-z-then-the-value-of-sin-x-y-sin-y-z-sin-x-sin-z-is-equal-to-

Question Number 102795 by saorey0202 last updated on 11/Jul/20

$$\mathrm{Points}\:{D},\:{E}\:\mathrm{are}\:\mathrm{taken}\:\mathrm{on}\:\mathrm{the}\:\mathrm{side}\:{BC} \\ $$$$\mathrm{of}\:\mathrm{a}\:\bigtriangleup\:{ABC},\:\mathrm{such}\:\mathrm{that}\:{BD}={DE}={EC}. \\ $$$$\mathrm{If}\:\:\angle{BAD}={x},\:\angle{DAE}={y},\:\angle{EAC}={z}, \\ $$$$\mathrm{then}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\:\:\frac{\mathrm{sin}\:\left({x}+{y}\right)\:\mathrm{sin}\left({y}+{z}\right)}{\mathrm{sin}\:{x}\:\mathrm{sin}\:{z}} \\ $$$$\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$

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