Maths-
General
Easy
Question
Assertion: If in a ABC ; = – and = ; || ||, then the value of cos 2A + cos 2B + cos 2C is – 1.
Reason: If in ABC, C = 90º, then cos 2A + cos 2B + cos 2C = – 1. - 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.
- 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 but (R) is not the correct explanation of (A).
= –
= –
= –
· =
= – = – (1 – 1) = 0
B = 90º
cos 2A + cos 2C = 2 cos (A + C) cos (A – C)
= 2 cos (180 – B) cos (A – C)
= 2 cos 90º cos (A – C) = 0
cos 2A + cos 2B + cos 2C = – 1
C = 90º
cos 2A + cos 2B = 2 cos (A + B) cos (A – B)= 0
cos 2A + cos 2B + cos 2C = – 1
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