Find an exact value. cosine of negative seven pi divided by twelve a) square root of six plus square root of two b) quantity square root of six minus square root of two divided by four c) square root of two minus square root of six d) quantity square root of two minus square root of six divided by four

The correct option is d

d) (√2 - √6) / 4

Step-by-step explanation:

The term given in the question is:

cos (-7π/12)

Solve the term by using scientific calculator:

cos (-7π/12) = (1 / 2√2) - (√3 / 2√2)

Mulitplying and dividing both terms on the right hand side of equality with 2√2:

(1 / 2√2) - (√3 / 2√2) = (1 / 2√2) (2√2 / 2√2) - (√3 / 2√2) (2√2 / 2√2)

(1 / 2√2) (2√2 / 2√2) - (√3 / 2√2) (2√2 / 2√2) = 2√2 / (2√2) ² - (2√2) (√3) / (2√2) ²

2√2 / (2√2) ² - (2√2) (√3) / (2√2) ² = 2√2 / (4) (2) - 2√6 / (4) (2)

2√2 / (4) (2) - 2√6 / (4) (2) = √2/4 - √6/4

√2/4 - √6/4 = (√2 - √6) / 4