Question

If 0 < b ≤ 90 and cos(11b + 2) = sin(12b − 4), what is the value of b? b = 3 b = 4 b = 5 b = 6

Answer 1

`b = 6`

Explanation:

Given

`0<b\le 90`

`\cos(11b + 2) = \sin(12b - 4)`

Required

Find b

To solve this, we make use of the following trigonometry rule:

If
`\cos(\alpha) = \sin(\beta)`

Then:
`\alpha + \beta = 90`

So:

`11b + 2 = 12b - 4`

Collect like terms

`11b - 12b = - 4 - 2`

`-b = - 6`

Multiply both sides by -1

`b = 6`