tan²A + cot²A = sec²A cosec²A - 2 prove it.

Answer :

Given 
tan²A + cot² A = Sec²A Cosec²A - 2

Taking L.H.S. 
$\Rightarrow$tan²A + cot² A 

$\Rightarrow$Sec²A - 1 + Cosec²A - 1                             ( As we know 1 + tan²A = Sec²A ,  1 + cot²A = Cosec²A  )

$\Rightarrow$Sec²A  + Cosec²A - 2 

$\Rightarrow$$\frac{1}{Co{s}^{2}A} + \frac{1}{Si{n}^{2}A}$  - 2

$\Rightarrow$$\frac{Si{n}^{2}A + Co{s}^{2}A}{Co{s}^{2}ASi{n}^{2}A }$  - 2

$\Rightarrow$$\frac{1}{Co{s}^{2}ASi{n}^{2}A }$ - 2

$\Rightarrow$Sec²A Cosec²A - 2 
Hence 
L.H.S.  = R.H.S.                            ( Hence proved )