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Trig Proof (1 Viewer)

Thread starter Lukybear
Start date Feb 1, 2010

L

Lukybear

Active Member

#1

Please help with this trignometric Proof:

$\frac{1+cosec^2A tan^2C}{1+cosec^2B tan^2 C} = \frac{1+cot^2A sin^2 C}{1 + cot^2B sin ^2 C}$

Last edited: Feb 1, 2010

Trebla

Administrator

Administrator

#2

$LHS = \dfrac{1 + cosec^2A.\tan^2C}{1 + cosec^2B.\tan^2C}\times\dfrac{cos^2C}{cos^2C}\\\\=\dfrac{\cos^2C + cosec^2A.\sin^2C}{\cos^2C + cosec^2B.\sin^2C}\\\\=\dfrac{\cos^2C + (1+\cot^2A).\sin^2C}{\cos^2C + (1+\cot^2B).\sin^2C}\\\\=\dfrac{\cos^2C + \sin^2C+\cot^2A.\sin^2C}{\cos^2C + \sin^2C+\cot^2B.\sin^2C}\\\\=\dfrac{1+\cot^2A.\sin^2C}{1+\cot^2B.\sin^2C}\\\\=RHS$

L

Lukybear

Active Member

#3

Is Latex Working. Somehow its not for me... I mean particularly the images

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