Select the answer which is equivalent to the given expression using your calculator. cos A=(63)/(65) and A is in Quadrant I. Find cos 2A. (1008)/(4225) (7426)/(4225) (3713)/(4225) (2016)/(4225)

Question

Select the answer which is equivalent to the given expression using your calculator.  cos A=(63)/(65) and A is in Quadrant I. Find  cos 2A.  (1008)/(4225)  (7426)/(4225)  (3713)/(4225)  (2016)/(4225)

Bytelearn · Accepted Answer

Given information: We are given that cos A = 63/65 and A is in Quadrant I. We need to find cos 2A. The double angle formula for cosine is cos 2A = cos^2 A - sin^2 A. Since we know cos A, we can find sin A using the Pythagorean identity sin^2 A + cos^2 A = 1.Find sin A: First, let's find sin A. We know that sin^2 A = 1 - cos^2 A. So we calculate sin^2 A = 1 - (63/65)^2.Calculate sin A: Calculating sin^2 A gives us sin^2 A = 1 - (3969/4225). We subtract 3969 from 4225 to find sin^2 A.Find cos 2A: Subtracting gives us sin^2 A = 4225/4225 - 3969/4225 = (4225 - 3969)/4225 = 256/4225.Use double angle formula: Now we take the square root to find sin A. Since A is in Quadrant I, sin A is positive. So sin A = sqrt(256/4225) = 16/65.Substitute values: Now we use the double angle formula for cosine: cos 2A = cos^2 A - sin^2 A. We substitute cos A = 63/65 and sin A = 16/65 into the formula.Calculate squares: Substituting the values gives us cos 2A = (63/65)^2 - (16/65)^2. We calculate each square separately.Subtract terms: Calculating the squares gives us cos 2A = (3969/4225) - (256/4225). We subtract the second term from the first term.Final result: Subtracting the terms gives us cos 2A = (3969 - 256)/4225 = 3713/4225.The value of cos 2A is 3713/4225, which matches one of the given answer choices.

Select the answer which is equivalent to the given expression using your calculator. $\cos A=\frac{63}{65}$ and A is in Quadrant I. $\newline$ Find $\cos 2 A$ . $\newline$ $\frac{1008}{4225}$ $\newline$ $\frac{7426}{4225}$ $\newline$ $\frac{3713}{4225}$ $\newline$ $\frac{2016}{4225}$

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