If x cosB - cosA = 0 and y sinB - cosA = 0, then the value of cos^2A will be

Answer 1

The two equations are

y sinB = cos A Equation 1

x cosB = cos A Equation 2

Is there a way to combine these two equations so that we can work with only one variable-either A or B?

One identity to use is Tan p = sin p / cos p.

Can you use the two equations to find Tan B? (Hint: divide the first by the second).

Now that you have your expression for Tan B, you can find an expression in terms of x and y for cos B (or sin B).

Method 1. Use a right triangle (remember tan B = opposite/adjacent) to determine the hypotenuse.

From this triangle, what is the expression for cos B?

Next, what is the expression for x cos B? This is one expression for cos A.

At this point, you can determine cos² A.

Method 2. Use the identity Tan²B + 1 = sec²B = 1/ cos²B.

From this, you should be able to see that cos²B = 1/(tan²B + 1).

Finally, use equation 2 from above to convert cos²B to cos²A.

Best wishes.

Answer 2

Your conditions tell us that cos A = x cos B = y sin B, so we would have

cos² A = xy cos B sin B = x² cos² B = y² sin² B

Does that help?