pls verify how (tan^(2)(θ))/(tan^(2)(θ)-1)+(csc^(2)(θ))/(sec^(2)(θ)-csc^(2)(θ))=1/(sin^(2)(θ)-cos^(2)(θ))?
This trignometry is a challenge to even the best of math freaks.. pls verify this complex equation
(tan^(2)(θ))/(tan^(2)(θ)-1)+(csc^(2)(θ))/(sec^(2)(θ)-csc^(2)(θ))=1/(sin^(2)(θ)-cos^(2)(θ))
Update:(tan^(2)(θ))/(tan^(2)(θ)-1)
+(csc^(2)(θ))/(sec^(2)(θ)-csc^(2)(θ))
=1/(sin^(2)(θ)-cos^(2)(θ))
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Your expression got cut off. Can you put additional information including the entire equation or identity or whatever it is supposed to be?
Multiply the first quotient on the left by cos²(Θ)/cos²(Θ) and the second by sin²(Θ)/sin²(Θ). Using the fact that tan(x) = sin(x)/cos(x) and csc(x) = 1/sin(x) leaves
sin²(Θ)/[sin²(Θ) - cos²(Θ)] + 1/[tan²(Θ) - 1]
Next, multiply the second term by cos²(Θ)/cos²(Θ) to get
sin²(Θ)/[sin²(Θ) - cos²(Θ)] + cos²(Θ)/[sin²(Θ) - cos²(Θ)] =
[sin²(Θ) + cos²(Θ)] / [sin²(Θ) - cos²(Θ)] =
1/[sin²(Θ) - cos²(Θ)]
which is the result that you want to reach.
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