Trigonometric identities and equations A level problem help

I can’t for the life of me figure out how to do this question. I have a feeling the first part involves sin/cos = tan. As for the second part in my textbook it has no questions similar to that at all. I’m doing edexcel A level maths

Help would really be appreciated

I can’t for the life of me figure out how to do this question. I have a feeling the first part involves sin/cos = tan.

As for the second part in my textbook it has no questions similar to that at all. I’m doing edexcel A level maths

Help would really be appreciated

Yes, for the first part, tan(2x) = sin(2x)/cos(2x) is how you want to start. Do that, and see if you can rearrange it into the given form.

For the second part, you know that solving the equation they ask you to solve is the same as solving (1 - 5cos(2x))sin(2x) = 0, and you know this even if you can't do part (a) since they have told you this is an alternative form of the question. How would you solve this? What do you know about any two things that multiply together to give you zero?

I tried doing fhat for the first part. I attached my workings. I really just have no clue

Circle line is correct. Just move everything onto the same side and factor out a common factor.

Thank you. Sometimes it just really isn’t clear what to do!

Refer to the result you're being asked to show. There are many suggestions on what you should do.

- The result you aim for is entirely in terms of sine and cosine. This suggests expressing tan(2x) in terms of sine and cosine, as you've done.

- The result has no denominators, this suggests multiplication through by cosine after the above step to get rid off this as a divisor.

- The result has a zero on one side, so you should just manipulate your answer and put all terms onto one side.

At this point it should be obvious that there is a common factor sin(2x) for you to factor out, just as the question has it.