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cris6969
28.07.2021 •
Mathematics
Find the general solution for:-
![sin\:x \:cos\: 3x+cos\:x\: sin\:3x=tan140](/tpl/images/2430/7656/fd244.png)
~Please show your work
~Thank you!
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Ответ:
Step-by-step explanation:
we would like to solve the following trigonometric equation:
the left hand side can be rewritten using angle sum indentity of sin which is given by:
therefore Let
Thus substitute:
simplify addition:
keep in mind that sin(t)=sin(π-t) saying that there're two equation to solve:
take inverse trig and that yields:
add π to both sides of the second equation and that yields:
sin function has a period of 2nπ thus add the period:
divide I equation by 4 and II by -4 which yields:
recall that,-½(nπ)=½(nπ) therefore,
by using a calculator we acquire:
hence,
the general solution for: for the trig equation are
Ответ:
216+36=252