Trig problems

[Gordo]

Hi guys, so I have been absent for quite a few days. I have no idea what is going on at the moment. Il give 3 examples of questions. Can you guys perhaps solve it and show steps and explain to me how you did it?
I have tried watching khan academy videos but it hasnt helped much.

Prove


1) 2tan(x) - sin2(x)/ 2sin(x)^2 = tan(x)




general solution


2) cos2(x) = cos(x) + 2




Prove
3) cos(50+x)cos(20+x) + sin(50+x)sin(20+x)= 3^1/2/2



thanks

 

[Deleted member 4993]

Hi guys, so I have been absent for quite a few days. I have no idea what is going on at the moment. Il give 3 examples of questions. Can you guys perhaps solve it and show steps and explain to me how you did it?
I have tried watching khan academy videos but it hasnt helped much.

Prove


1) 2tan(x) - sin2(x)/ 2sin(x)^2 = tan(x) ................ Check this problem for accuracy

Hint:

sin(2Θ) = 2 * cos(Θ) *sin(Θ)


general solution


2) cos2(x) = cos(x) + 2

Hint:

cos(2Θ) = 2 * cos²(Θ) - 1




Prove
3) cos(50+x)cos(20+x) + sin(50+x)sin(20+x)= 3^1/2/2

hint:

cos(A-B) = cos(A) * cos(B) + sin(A) * sin(B)

thanks

Please use grouping symbols to assign hierarchy of arithmetical operations. For example, the right hand side of the prob.#3 as written is:

3¹ ÷ 2 ÷ 2

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