from the question cos(x) [ cos(x) + 2sin(x) ] = 1 , so cos(x)=1It would really help to know the question.
And how did you conclude that the answer required cos(x) to be 1. That leads to one set of answers, but does it lead to every answer?
Have you tried doing what they say to do? I don't think I've seen you or anyone else do the first step. It does work, and you'll probably learn what they intend for you to learn if you try that.part (b) has 5 answers, and I can only get some but not all 5 answers.
How to get all 5 answers by using the expression of cos(x) + 2sin(x) = r cos (x-y) ?
Thank you for your guidance.Have you tried doing what they say to do? I don't think I've seen you or anyone else do the first step. It does work, and you'll probably learn what they intend for you to learn if you try that.
What do you get for r and y? If you can't do that yet, though they clearly have taught you how, please show the method they teach, as I have seen some very different approaches. It will be best if we don't confuse you with a method you haven't seen.
Once you have that, when you rewrite equation (b) using this, it will look like
r cos(x) cos(x-y) = 1
where r and y are constants you will know. What I would do next is to use the product-to-sum formula,
cos(a)cos(b) = [cos(a-b) + cos(a+b)]/2
This turns out to result in an equation you can solve directly.
Are you familiar with that formula? If not, then let us know what you have learned, so we can guide you along the path they have set for you.