Question

What is the exact value of Cosine (StartFraction 11 pi Over 21 EndFraction) cosine (StartFraction pi Over 7 EndFraction) minus sine (StartFraction 11 pi Over 21 EndFraction) sine (StartFraction pi over 7 EndFraction)?

Negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction
Negative one-half
One-half
StartFraction StartRoot 3 EndRoot Over 2 EndFraction

Answer 1

B. -1/2

Explanation:

on edge

Answer 2

Option (2)

Explanation:

Given trigonometric expression is,

`\text{cos}((11\pi)/(21))\text{cos}((\pi)/(7))-\text{sin}((11\pi)/(21))\text{sin}((\pi)/(7))`

This expression is in the form of an identity,

cos(A + B) = cos(A)cos(B) - sin(A)sin(B)

By substituting the values of A =
`(11\pi)/(21)` and B =
`(\pi)/(7)` in the identity,

`\text{cos}((11\pi)/(21))\text{cos}((\pi)/(7))-\text{sin}((11\pi)/(21))\text{sin}((\pi)/(7))` = cos
`((11\pi)/(21)+(\pi)/(7))`

= cos
`((11\pi+3\pi)/(21))`

= cos
`((14\pi)/(21))`

= cos
`((2\pi)/(3))`

= -
`(1)/(2)`

Therefore, Option (2) will be the answer.