Original post by Awor patience

Solve cos(x+30)-sinx

Help

Well, this is not an equation, so you can't really solve it...

But if you've typo'd the "=" as "-", consider turning cosine into sine (or the other way round) using an identity (which one? There should be one in your notes/book).

But if you've typo'd the "=" as "-", consider turning cosine into sine (or the other way round) using an identity (which one? There should be one in your notes/book).

I'm assuming this is supposed to be cos(x+30) = sin(x)?

You could then probably use the compound angle formula for cos and get √3/2 cos(x) - 1/2 sin(x) = sin(x)

√3 cos(x) = 3 sin(x)

then you can rearrange to get an equation in tan(x) and solve for x

(With the identity of tan(x) = sin(x)/cos(x))

Alternatively you could use that cos(x-90) = sin(x)

This would give sin(x+120) = sin(x) and this is another thing that could be easily worked out using a geometric approach

You could then probably use the compound angle formula for cos and get √3/2 cos(x) - 1/2 sin(x) = sin(x)

√3 cos(x) = 3 sin(x)

then you can rearrange to get an equation in tan(x) and solve for x

(With the identity of tan(x) = sin(x)/cos(x))

Alternatively you could use that cos(x-90) = sin(x)

This would give sin(x+120) = sin(x) and this is another thing that could be easily worked out using a geometric approach

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