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write sec^2x = .... ?

1/cos^2x

1+ tan^2 x ?

sec^2x

then you can use directly here, tan x cot x =1

All you need to know is the definition of \(\tan x, \cot x, \sec x\) and how to work with fractions.

yes, so i said to replace sec^2 x by 1+tan^2x

can be solved without involving fractions ... :)

@koli123able did you try ?

which side to choose?

right ...?

cotx * sec^2x=cotx * (1+tan^2 x) =..... ?

cotx+ cotx tan^2x

cotx tanx becomes 1

cotx+ cotx tan^2x = cot x + tan x (cot x tan x)

is that an identity cot x tanx =1 ??

absolutely.
tan x = 1/cot x
so, tan x cot x =1

cosx/sinx =sinx/cosx

cos^2x + sin^2x / cosx sinx

1/cosxsinx

cscx+secx