cos a = 3/4
Step-by-step explanation:
Step 1: Given details are cos(a)^4 - sin(a)^4 = 1/8
Now, cos(a)^4 can also be written as (cos²a)² and sin(a)^4 can be written as (sin²a)²
⇒ (cos²a)² - (sin²a)² = 1/8
Step 2: Apply the formula for a² - b² = (a - b) (a + b). Here a = cos²a and b = sin²a
⇒ (cos²a)² - (sin²a)² = (cos²a - sin²a) (cos²a + sin²a) = 1/8
⇒ (cos²a - sin²a) = 1/8 since cos²a + sin²a = 1
⇒ cos²a - (1 - cos²a) = 1/8 since sin²a = 1 - cos²a
⇒ 2 cos²a - 1 = 1/8
⇒ 2 cos²a = 1 + 1/8 = 9/8
⇒ cos²a = 9/16
⇒ cos a = 3/4
Answer:
Step-by-step explanation:
cos(a)^4 - sin(a)^4 = 1/8
(cos(a)² - sin(a)²)×(cos(a)²+ sin(a)²)= 1/8 ; {remember: cos(a)²+ sin(a)² = 1}
(cos(a)² - sin(a)²) = 1/8
cos(a)² - (1 - (cos(a)² = 1/8
2cos(a)² = 9/8
2cos(a)² = 9/16
cosa = ±3/4
