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Question : 21 of 160
Marks:
+1,
-0
Solution:
Consider the expression,
A+B+C=Ï€ Then,
sin(−A)‌sin(−B )‌sin(−C) =− ()3(cos‌A−sin‌A)(cos‌B−sin‌B) (cos‌C−sin‌C)=− cos‌A‌cos‌B‌cos‌C(1−tan‌A) (1−tan‌B)(1−tan‌C)=−1 cos‌A‌cos‌B‌cos‌C(1−tan‌A−tan‌B−tan‌C +tan‌A‌tan‌B+tan‌B‌tan‌C+tan‌A‌tan‌C −tan‌A‌tan‌B‌tan‌C) =cos‌A+B+C‌‌‌[∵A+B+C=π] Further simplify above,
−2(tan‌A+tan‌B+tan‌C) =−2(tan‌A‌tan‌B+tan‌B‌tan‌C+tan‌A‌tan‌C) tan‌A‌tan‌B+tan‌B‌tan‌c+tan‌A‌tan‌C =tan‌A+tan‌B+tan‌C
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