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Jika sin (x+15°) = α dengan 0° ≤ x ≤ 15° , maka sin (2x+60°) adalah ....
Jika sin (x+15°) = α dengan 0° ≤ x ≤ 15° , maka sin (2x+60°) adalah ....
ImmanuelSinaga
![$\begin{align}sin~(2x+60)~~~&=~sin~(2(x+15)+30)) \\ &=~sin~2(x+15)~cos~30+sin~30~cos~2(x+15) \\ &=~2~sin~(x+15)~cos~(x+15)~cos~30~ \\ &~~~~~+~sin~30~[cos^2(x+15)-sin^2(x+15)] \\ &=~a.\sqrt{1-a^2}.\sqrt{3}~+~\frac{1}{2}-\frac{1}{2}a^2-\frac{1}{2}a^2 \\ &=~\sqrt{3-3a^2}~a~+~\frac{1}{2}~-~a^2\end{align}](https://tex.z-dn.net/?f=%24%5Cbegin%7Balign%7Dsin%7E%282x%2B60%29%7E%7E%7E%26%3D%7Esin%7E%282%28x%2B15%29%2B30%29%29+%5C%5C+%26%3D%7Esin%7E2%28x%2B15%29%7Ecos%7E30%2Bsin%7E30%7Ecos%7E2%28x%2B15%29+%5C%5C+%26%3D%7E2%7Esin%7E%28x%2B15%29%7Ecos%7E%28x%2B15%29%7Ecos%7E30%7E+%5C%5C+%26%7E%7E%7E%7E%7E%2B%7Esin%7E30%7E%5Bcos%5E2%28x%2B15%29-sin%5E2%28x%2B15%29%5D+%5C%5C+%26%3D%7Ea.%5Csqrt%7B1-a%5E2%7D.%5Csqrt%7B3%7D%7E%2B%7E%5Cfrac%7B1%7D%7B2%7D-%5Cfrac%7B1%7D%7B2%7Da%5E2-%5Cfrac%7B1%7D%7B2%7Da%5E2+%5C%5C+%26%3D%7E%5Csqrt%7B3-3a%5E2%7D%7Ea%7E%2B%7E%5Cfrac%7B1%7D%7B2%7D%7E-%7Ea%5E2%5Cend%7Balign%7D "$\begin{align}sin~(2x+60)~~~&=~sin~(2(x+15)+30)) \\ &=~sin~2(x+15)~cos~30+sin~30~cos~2(x+15) \\ &=~2~sin~(x+15)~cos~(x+15)~cos~30~ \\ &~~~~~+~sin~30~[cos^2(x+15)-sin^2(x+15)] \\ &=~a.\sqrt{1-a^2}.\sqrt{3}~+~\frac{1}{2}-\frac{1}{2}a^2-\frac{1}{2}a^2 \\ &=~\sqrt{3-3a^2}~a~+~\frac{1}{2}~-~a^2\end{align}")
1 votes
Thanks 5
Ika05
Thx a lot kak :)
ImmanuelSinaga
iya
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