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



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mahmit2012
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Is this equation or identity?

logynklode
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Verify each trigonometric equation by substituting identities to match the right hand side of the equation to the left hand side of the equation.

ganeshie8
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\(\cot x \sec^4 x = \cot x + 2 \tan x + \tan^3 x \)

ganeshie8
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its like above ?

logynklode
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huh?

ganeshie8
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*the equation u seeing in ur assessment sheet, is it like the one ive posted above ?

logynklode
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its tan cubed x at the end other then that yes

ganeshie8
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ok thnks :)
pick the side that has more terms, and do SOMETHING and try getting to the other side

ganeshie8
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here, the right side has more terms, right ?

logynklode
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what? the irght side has more terms yeah

ganeshie8
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ya so we start with that side, and work, and prove that it equals left side.

logynklode
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okay

ganeshie8
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\(\cot x + 2\tan x + \tan^3 x\)
\(\frac{1}{\tan x} + 2\tan x + \tan^3 x\)
\(\frac{1+ 2\tan^2 x + \tan^4 x}{\tan x}\)
\(\frac{1+ \tan^2 x + \tan^2x + \tan^4 x}{\tan x}\)
\(\frac{\sec^2 x + \tan^2x + \tan^4 x}{\tan x}\)
\(\frac{\sec^2 x + \tan^2x(1 + \tan^2 x)}{\tan x}\)
\(\frac{\sec^2 x + \tan^2x(\sec^2 x)}{\tan x}\)
\(\frac{\sec^2 x(1 + \tan^2x)}{\tan x}\)
\(\frac{\sec^2 x(\sec^2 x)}{\tan x}\)
\(\frac{\sec^4 x}{\tan x}\)
\(\cot x\sec^4 x\)
= LEFT HAND SIDE

ganeshie8
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thats the complete solution; see if it makes sense

jishan
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good solve ganeshie.,...........

rubypearl11
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How did you get rid of the tan^4x? @ganeshie8?

mayaal
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@ganeshie8 i dont understand ur solution

ganeshie8
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hmm which line ?

mayaal
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the 3rd line from the end.

ganeshie8
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\[\large \frac{\sec^2 x + \tan^2x(\sec^2 x)}{\tan x}\]

ganeshie8
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you're fine, till this line ?

mayaal
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yes

ganeshie8
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good, next factor out `sec^2x` from both terms, you get :
\[\large \frac{\sec^2 x(1 + \tan^2x)}{\tan x}\]

ganeshie8
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still fine ?

mayaal
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oh,ok.so u factored out the sec^2x from the whole numerator?

ganeshie8
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exactly !

mayaal
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great!thnku very much @ganeshie8

ganeshie8
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np :)