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Question : 22 of 160
Marks:
+1,
-0
Solution:
A+B+C= A+B=−C cos(A+B)=cos(−C)=−sin‌C Now,
cos‌2‌A+cos‌2‌B+cos‌2‌C =2‌cos(A+B)‌cos(A−B)+cos‌2‌C =2(−sin‌C)‌cos(A−B)+cos‌2‌C =−2‌sin‌C‌cos(A−B)+1−2sin2C =1−2‌sin‌C(cos(A−B)+sin‌C) =1−2‌sin‌C[cos(A−B)+sin(−(A+B))] =1−2‌sin‌C[cos(A−B)+(−cos(A+B)] =1−2‌sin‌C[cos(A−B)−cos(A+B)] =1−2‌sin‌C[2‌sin‌A‌sin‌B] =1−4‌sin‌A‌sin‌B‌sin‌C
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