Answer :
All values of x in the interval [0, 2] that satisfy the equation are [tex]\frac{\pi }{2} ,3\frac{\pi }{2}[/tex].
What is an equation?
A mathematical equation is a formula that uses the equals symbol (=) to connect two expressions and express their equality. A well-formed formula consisting of two expressions linked by an equals sign is considered to be an equation in English, but the word's cognates in other languages may have slightly different definitions. For instance, an équation is defined as having one or more variables in French.
The first step in resolving a variable equation is to identify the values of the variables that lead to the equality being true. The variables that must be changed in order to solve the equation are referred to as the unknowns, and the values of the unknowns that satisfy the equality are referred to as the equation's solutions.
Calculations:
16cos(x +8sin(2x)=0
Divide by 8
2cos(x)+sin(2x)=0
Identity:
sin(2x)=2sin(x)cos(x)
2cos(x)+2sin(x)cos(x)=0
Factor:
2cos(x)(1+sin(x))=0
2cos(x)=0
cos(x)=0=x=[tex]\frac{\pi }{2}[/tex],3[tex]\frac{\pi }{2}[/tex]
(1+sin(x))=0
sin(x)=−1=x=3[tex]\frac{\pi }{2}[/tex]
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