Question

prove that cosec 2A +Cot 2A =cot A
Please help with this trigonometry problem asap

Answer 1

cosec2a+cot2a
  =1/sin2a + 1/tan2a
  =1/sin2a + cos2a/sin2a
   = (1+cos2a)/sin2a
   =(1 + 2cos^2a -1)/sin2a
   =(2cos^2a)/sin2a
   = (2.cosa.cosa)/2.sina.cosa
   =cosa/sina
   =cota
   FORMULA USED:
  tan2a=sin2a/cos2a
   sin2a=2sinacosa
   cos2a=2cos^2a - 1
   cota=cosa/sina

Answer 2

Answer and Explanation:

To prove : $\csc 2A+\cot 2A=\cot A$

Proof :

Taking LHS,

$LHS=\csc 2A+\cot 2A$

$=\frac{1}{\sin 2A}+\frac{\cos 2A}{\sin 2A}$

Taking LCM,

$=\frac{1+\cos 2A}{\sin 2A}$

Applying formula,

$1+\cos 2x=2\cos^2 x\\\sin 2x=2\sin x\cos x$

$=\frac{2\cos^2 A}{2\sin A\cos A}$

$=\frac{\cos A}{\sin A}$

$=\cot A$

= RHS

Hence proved, LHS=RHS