anonymous
  • anonymous
Verify each trigonometric equation by substituting identities to match the right hand side of the equation to the left hand side of the equation. 1. cot x sec4x = cot x + 2 tan x + tan3x
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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zepdrix
  • zepdrix
Are those exponents or coefficients? \(\large \cot x\sec^4x\) or \(\large \cot x\sec4x\) ?
anonymous
  • anonymous
exponents
zepdrix
  • zepdrix
Oh ok, now this problem makes more sense :)

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zepdrix
  • zepdrix
Here is an important identity we'll want to use, \[\large \color{green}{\sec^2x=1+\tan^2x}\] So let's start here,\[\large \cot x\left(\sec^4x\right) \qquad=\qquad \cot x \left(\color{green}{\sec^2x}\right)^2\] Understand what I did with the exponent?
anonymous
  • anonymous
no
anonymous
  • anonymous
did u factor it
zepdrix
  • zepdrix
Rule of exponents: \(\large (x^a)^b =x^{ab}\) We're using this rule in reverse, \(\large x^4\qquad=\qquad x^{2\cdot2}\qquad=\qquad (x^2)^2\)
anonymous
  • anonymous
ok i get it now
zepdrix
  • zepdrix
I colored the inside portion green, see how we'll apply the identity?
anonymous
  • anonymous
ok
zepdrix
  • zepdrix
\[\large \cot x \left(\color{green}{\sec^2x}\right)^2\qquad=\qquad \cot x \left(\color{green}{1+\tan^2x}\right)^2\] From here, expand the outer square, the black one.
zepdrix
  • zepdrix
In case you're confused about what I'm asking, \[\large \cot x \left(\color{green}{1+\tan^2x}\right)^2\qquad=\qquad \cot x \left(\color{green}{1+\tan^2x}\right)\left(\color{green}{1+\tan^2x}\right)\] The next step is to multiply out the brackets.
anonymous
  • anonymous
ok

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