Question

Find the value of cos(a), if cos(a)^4 - sin(a)^4 = 1/8

Answer 1

cosa = ±3/4

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

Answer 2

cos a = 3/4

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