Final answer:
Solving for cos A when given cos 2A = 11/25 involves using the double-angle formula for cosine. Upon solving, we find that cos A = ±(3/5)√2. However, the proposed value of cos A = 6/5√2 is incorrect as it exceeds 1, which is not possible for cosine values.
Step-by-step explanation:
If cos 2A = 11/25, we can use the double-angle formula for cosine to express cos 2A in terms of cos A. Recall that the double-angle formula for cosine is given by:
cos 2A = 2 cos² A - 1
Given that cos 2A = 11/25, we can rearrange the formula to solve for cos A:
11/25 = 2 cos² A - 1
Adding 1 to both sides:
11/25 + 1 = 2 cos² A
36/25 = 2 cos² A
Divide both sides by 2 to isolate cos² A:
cos² A = 36/50
cos² A = 18/25
Now, take the square root of both sides:
cos A = ±√(18/25)
cos A = ±(3/5)√2
Since cosine can be positive or negative depending on the quadrant A is in, we have two possible values. However, if we use the relation cos A = Ax/A within a right triangle (where Ax is the adjacent side and A is the hypotenuse), we understand that the cosine of an angle must be <= 1, which suggests the correct answer is cos A = 6/5√2. However, this value is incorrect since 6/5√2 is greater than 1, which is not possible for cosine values.