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Exercise

$sen\:60^{\circ}cos\:30^{\circ}$

Step-by-step Solution

1

Apply the trigonometric identity: $\sin\left(x\right)\cos\left(y\right)$$=\frac{\sin\left(x+y\right)+\sin\left(x-y\right)}{2}$, where $x=60$ and $y=30$

$\frac{\sin\left(60+30\right)+\sin\left(60-30\right)}{2}$
2

Add the values $60$ and $30$

$\frac{\sin\left(90\right)+\sin\left(60-30\right)}{2}$
3

Add the values $60$ and $-30$

$\frac{\sin\left(90\right)+\sin\left(30\right)}{2}$
4

The sine of $90$ equals $1$

$\frac{1+\sin\left(30\right)}{2}$

Final answer to the exercise

$\frac{1+\sin\left(30\right)}{2}$

Try other ways to solve this exercise

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  • Integrate using basic integrals
  • Verify if true (using algebra)
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  • FOIL Method
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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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