Trigonometric Identity (3 Problems, Please help <3 )

[Lemon]

Hey guys/girls i'm new to this forum, but the way i see you help each other out is very motivating and i wanted to get in on this

Anyways, i have 3 trigonometric identity problems i simply don't understand, am i not seeing something? Please help me out!

Here are a few screenshots of the questions themselves, the reason why i am posting screenshots is because it's from maths online and they tell you how to do it, but i still don't understand =\


In the one above i am simply lost






I know it shows me how to do it, but i don't understand how they convert into what they are converted into, please help and thankyou guys!!

 

[Unknown008]

I see only two problems, the first showing the how to approach and the actual method.

What you need to know are the basic identities.

\(\displaystyle \cos^2\theta + \sin^2\theta = 1\)

This is one of them. One can prove it through the Pythagora's Theorem.

Next, you will have to practice and get some sort of intuition on what you should do next to arrive to the final answer.

Trust me, I too found it quite impossible to do when I first worked with identities to be proved. But then, with practice, I started to get the hang of it, even though I can assure that there will be identities which are challenging and will require a lot of effort from you. I don't want to discourage you, but just practice and you'll get the better out of the identities thrown to you

 

[Lemon]

I see only two problems, the first showing the how to approach and the actual method.

What you need to know are the basic identities.

\(\displaystyle \cos^2\theta + \sin^2\theta = 1\)

This is one of them. One can prove it through the Pythagora's Theorem.

Next, you will have to practice and get some sort of intuition on what you should do next to arrive to the final answer.

Trust me, I too found it quite impossible to do when I first worked with identities to be proved. But then, with practice, I started to get the hang of it, even though I can assure that there will be identities which are challenging and will require a lot of effort from you. I don't want to discourage you, but just practice and you'll get the better out of the identities thrown to you

Thanks I sure have been and now i'm much better

 

[Lemon]

Identity crisis?

Haha