Can anyone help me with this trig? Supposedly we have to make the left side to be what it is on the right side.. but no matter what i tried, it just work. Can anyone show me the steps?
Formulas:
Secθ=1/Cosθ
Cscθ=1/Sinθ
Cotθ=1/Tanθ

Tanθ=Sinθ/Cosθ
Cotθ=Cosθ/Sinθ

Sin²θ+Cos²θ=1
Tan²θ+1=Sec²θ
1+Cot²θ=Csc²θ

Problem: Verify the Identity.
((1+cos3t)/sin3t)+(sin3t/(1+cos3t))=2csc3t

Question

Can anyone help me with this trig? Supposedly we have to make the left side to be what it is on the right side.. but no matter what i tried, it just work. Can anyone show me the steps?
Formulas:
Secθ=1/Cosθ
Cscθ=1/Sinθ
Cotθ=1/Tanθ

Tanθ=Sinθ/Cosθ
Cotθ=Cosθ/Sinθ

Sin²θ+Cos²θ=1
Tan²θ+1=Sec²θ
1+Cot²θ=Csc²θ

Problem: Verify the Identity.
((1+cos3t)/sin3t)+(sin3t/(1+cos3t))=2csc3t

anonymous · Answer

*Just doesn't work

anonymous · Answer

the eq. has to be just inspected wrt RHS,  conclusions: The LHS should be in terms of csc3t => 1/sin3t


LHS:

(1/sin3t) + (cos3t/sin3t) + ((sin3t)/(1+cos3t))
Now you got half of the war cut down, as you can see that you already got 1 term 1/sin3t So all you need to work out is how you gona get another 1/sin3t to make the equality.

take the LCM of the 2nd and 3rd term  and you will get

1/sin3t + [cos3t + cos^2(3t) + sin^2(3t)]/sin3t(1 + cos3t)

by which the second term will simplify to 1/sin3t & you get the answer = 2/csc3t.

anonymous · Answer

Thank you very much! i greatly appreciate your help!