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cot x sec4x = cot x + 2 tan x + tan3x

Mathematics
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Is this equation or identity?
Verify each trigonometric equation by substituting identities to match the right hand side of the equation to the left hand side of the equation.
\(\cot x \sec^4 x = \cot x + 2 \tan x + \tan^3 x \)

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Other answers:

its like above ?
huh?
*the equation u seeing in ur assessment sheet, is it like the one ive posted above ?
its tan cubed x at the end other then that yes
ok thnks :) pick the side that has more terms, and do SOMETHING and try getting to the other side
here, the right side has more terms, right ?
what? the irght side has more terms yeah
ya so we start with that side, and work, and prove that it equals left side.
okay
\(\cot x + 2\tan x + \tan^3 x\) \(\frac{1}{\tan x} + 2\tan x + \tan^3 x\) \(\frac{1+ 2\tan^2 x + \tan^4 x}{\tan x}\) \(\frac{1+ \tan^2 x + \tan^2x + \tan^4 x}{\tan x}\) \(\frac{\sec^2 x + \tan^2x + \tan^4 x}{\tan x}\) \(\frac{\sec^2 x + \tan^2x(1 + \tan^2 x)}{\tan x}\) \(\frac{\sec^2 x + \tan^2x(\sec^2 x)}{\tan x}\) \(\frac{\sec^2 x(1 + \tan^2x)}{\tan x}\) \(\frac{\sec^2 x(\sec^2 x)}{\tan x}\) \(\frac{\sec^4 x}{\tan x}\) \(\cot x\sec^4 x\) = LEFT HAND SIDE
thats the complete solution; see if it makes sense
good solve ganeshie.,...........
How did you get rid of the tan^4x? @ganeshie8?
@ganeshie8 i dont understand ur solution
hmm which line ?
the 3rd line from the end.
\[\large \frac{\sec^2 x + \tan^2x(\sec^2 x)}{\tan x}\]
you're fine, till this line ?
yes
good, next factor out `sec^2x` from both terms, you get : \[\large \frac{\sec^2 x(1 + \tan^2x)}{\tan x}\]
still fine ?
oh,ok.so u factored out the sec^2x from the whole numerator?
exactly !
great!thnku very much @ganeshie8
np :)

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