If sin x = 12/13, where 0° < x < 90°, find the value of 1 - cos\(^2\)x
Answer Details
We know that sin x = opposite/hypotenuse = 12/13, therefore, the adjacent side of the right-angled triangle is √(13^2 - 12^2) = 5.
Now, we need to find the value of 1 - cos^2x. Using the identity sin^2x + cos^2x = 1, we can write:
cos^2x = 1 - sin^2x
Substituting sin x = 12/13, we get:
cos^2x = 1 - (12/13)^2
cos^2x = 1 - 144/169
cos^2x = 25/169
Therefore, 1 - cos^2x = 1 - 25/169 = 144/169.
Hence, the answer is (d) 144/169.