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Exercise

$2cos^2z+11cosz+14$

Step-by-step Solution

1

Applying the pythagorean identity: $\cos^2(\theta)=1-\sin(\theta)^2$

$2\left(1-\sin\left(z\right)^2\right)+11\cos\left(z\right)+14$
Why is 1 - sin(x)^2 = cos(x)^2 ?
2

Multiply the single term $2$ by each term of the polynomial $\left(1-\sin\left(z\right)^2\right)$

$2-2\sin\left(z\right)^2+11\cos\left(z\right)+14$
3

Add the values $2$ and $14$

$16-2\sin\left(z\right)^2+11\cos\left(z\right)$

Final answer to the exercise

$16-2\sin\left(z\right)^2+11\cos\left(z\right)$

Try other ways to solve this exercise

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  • Find the derivative
  • Integrate using basic integrals
  • Verify if true (using algebra)
  • Verify if true (using arithmetic)
  • Integrate by partial fractions
  • Product of Binomials with Common Term
  • FOIL Method
  • Integrate by substitution
  • Integrate by parts
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