Question

Angles α and β are the two acute angles in a right triangle. Use the relationship between sine and cosine to find the value of α if α < β. sin(2x − 8) = cos(6x − 6)

Answer 1

A

Explanation:

Answer 2

The value of angle α is 18 degree.

Explanation:

Given information: Angles α and β are the two acute angles , α < β.

Given equation is

`\sin (2x-8)=\cos (6x-6)`

`\cos (90-(2x-8))=\cos (6x-6)`
`[\because \sin (90-x)=\cos x]`

Equating both sides.

`90-2x+8=6x-6`

`98+6=6x+2x`

`104=8x`

`13=x`

The value of x is 13.

The measure of angles is

`2x-8=2(13)-8=18`

`6x-6=6(13)-6=72`

Since 18<72, therefore the value of angle α is 18 degree.