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Exercise

$2\sin^2\left(x\right)+7\sin\left(x\right)+6$

Step-by-step Solution

1

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

$2\left(1-\cos\left(x\right)^2\right)+7\sin\left(x\right)+6$
Why is 1 - cos(x)^2 = sin(x)^2 ?
2

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

$2-2\cos\left(x\right)^2+7\sin\left(x\right)+6$
3

Add the values $2$ and $6$

$8-2\cos\left(x\right)^2+7\sin\left(x\right)$

Final answer to the exercise

$8-2\cos\left(x\right)^2+7\sin\left(x\right)$

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
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Similar Questions Solved

$\left(\sin\left(x\right)+\cos\left(x\right)\right)^2$

$1+cot^2x$

$tan\left(x\right)csc\left(x\right)$

$\tan\left(x\right)\csc\left(x\right)$

$\frac{2+\tan^2\left(x\right)}{\sec^2\left(x\right)}-1$

$csc^2x-1$

$\frac{2+tan^2x}{sec^2x}-1$

Main Topic: Simplify Trigonometric Expressions

Simplification of trigonometric expressions consists of rewriting an expression with trigonometric functions in a simpler form. To perform this task, we usually use the most common trigonometric identities, and some algebra.

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