Question

If sin A = 1/3 , find tan 3A and cos 3A .

a) tan 3A = 3/10 , cos 3A = 27/100

b) tan 3A = 1/10 , cos 3A = 27/100

c) tan 3A = 3/10 , cos 3A = 9/10

d) tan 3A = 1/10 , cos 3A = 9/10

Answer 1

To find tan 3A and cos 3A, we can use trigonometric identities. Using the value of sin A = 1/3, we can use the identities tan 2A = (2tan A) / (1 - tan² A) and cos 2A = cos² A - sin² A to find the values of tan 3A and cos 3A.

Step-by-step explanation:

To find tan 3A and cos 3A, we'll use trigonometric identities. First, we know that sin A = 1/3. Using the identity tan 2A = (2tan A) / (1 - tan² A), we can find tan 3A. Plugging in tan A = sin A / cos A = (1/3) / sqrt(1 - (1/3)²) = 1/ √8 / 3 = √8 / 3, we get tan 3A = (2 * (√8 / 3)) / (1 - (√8 / 3)²) = (2√8 / 3) / (1 - 8 / 9) = (2√8 / 3) / (1/9) = (2√8 / 3) * 9 = 6√8.

Next, using the identity cos 2A = cos² A - sin² A, we can find cos 3A. Plugging in cos A = sqrt(1 - sin² A) = √(1 - 1/9) = √8/3, we get cos 3A = cos² A - sin² A = (√8/3)² - (1/3)² = 8/3 - 1/9 = 24/9 - 1/9 = 23/9.