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# Proving trigonometric equation/identity and one about solving. watch

1. 1st question is: sin( theta+pi/6)=3cos(theta-pi/6) in the range -180 to 180.
2nd question is : cos(x+pi/6)+sin(x+pi/3)= root3cosx

I have tried messing around with identities to see if it works but have failed so far , i tried using double angle identities but the way i rearranged didn't meet the requirements so they didn't work either. Don't know what to do.
2. (Original post by Nirm)
1st question is: sin( theta+pi/6)=3cos(theta-pi/6) in the range -180 to 180.
2nd question is : cos(x+pi/6)+sin(x+pi/3)= root3cosx

I have tried messing around with identities to see if it works but have failed so far , i tried using double angle identities but the way i rearranged didn't meet the requirements so they didn't work either. Don't know what to do.
compound identities first
3. (Original post by TeeEm)
compound identities first
Okay i did that for question 1 but cant figure anything out from then onwards
4. (Original post by Nirm)
Okay i did that for question 1 but cant figure anything out from then onwards
You do know what cos and sin of pi/6 are don't you?
5. (Original post by Nirm)
Okay i did that for question 1 but cant figure anything out from then onwards
both work the same way

look at some examples of similar questions in the following PDF

PDF.pdf

hope it is useful
6. (Original post by TenOfThem)
You do know what cos and sin of pi/6 are don't you?
Just face palmed my self, completely forgot about the special triangles. Now i can solve it
Thanks you!
7. (Original post by Nirm)
Just face palmed my self, completely forgot about the special triangles. Now i can solve it
Thanks you!

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