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Exercise

$-cos\left(\frac{\pi}{2}+x\right)$

Step-by-step Solution

1

Using the cosine of a sum formula: $\cos(\alpha\pm\beta)=\cos(\alpha)\cos(\beta)\mp\sin(\alpha)\sin(\beta)$, where angle $\alpha$ equals $\frac{\pi }{2}$, and angle $\beta$ equals $x$

$-\left(\cos\left(\frac{\pi }{2}\right)\cos\left(x\right)-\sin\left(\frac{\pi }{2}\right)\sin\left(x\right)\right)$
2

The sine of $\frac{\pi }{2}$ equals $1$

$-\left(\cos\left(\frac{\pi }{2}\right)\cos\left(x\right)- 1\sin\left(x\right)\right)$
3

Multiply $-1$ times $1$

$-\left(\cos\left(\frac{\pi }{2}\right)\cos\left(x\right)-\sin\left(x\right)\right)$
4

The cosine of $\frac{\pi }{2}$ equals $0$

$-\left(0\cos\left(x\right)-\sin\left(x\right)\right)$
5

Any expression multiplied by $0$ is equal to $0$

$-\left(-\sin\left(x\right)\right)$

Final answer to the exercise

$-\left(-\sin\left(x\right)\right)$

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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Similar Questions Solved

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

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

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

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

$csc^2x-1$

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

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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