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

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

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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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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