Question

Given that sin(x+4)=cos(3x)find tan(x+40)to 4 s.f.​

Answer 1

`\tan(x + 40) = 1.842`

Explanation:

Given

`\sin(x + 4) = \cos(3x)`

Required

Find
`\tan(x + 40)`

In trigonometry

If
`\sin(A) = \cos(B)`

Then:
`A + B = 90`

So, we have:

`\sin(x + 4) = \cos(3x)`

`3x + x + 4 = 90`

`4x + 4 = 90`

Collect like terms

`4x =- 4 + 90`

`4x =86`

Solve for x

`x = 86/4`

`x = 21.5`

So:

`\tan(x + 40) = \tan(21.5+40)`

`\tan(x + 40) = \tan(61.5)`

Using a calculator:

`\tan(x + 40) = 1.842`