Maths-
General
Easy
Question
Assertion: In any triangle a cos A + b cos B + c cos 
Reason: In any trianglesinsinsin 
- If both (A) and (R) are true, and (R) is the correct explanation of (A).
- If both (A) and (R) are true but (R) is not the correct explanation of (A).
- If (A) is true but (R) is false.
- If (A) is false but (R) is true.
The correct answer is: If both (A) and (R) are true, and (R) is the correct explanation of (A).
The inequality in reason R is an inequality of symmetric function in a triangle (Recall that any symmetric function of sine or cosine attains maximum value in an equilateral triangle).
Now the inequality given in assertion A is
2R sin A cos A + 2R sin B cos B + 2R sin C cos C ≤ 2R (sin A + sin B + sin C)
or sin 2A + sin 2B + sin 2C ≤ 2(sinA + sin B + sin C)
Thus assertion R is true and follows from reason R.
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