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Lena [83]
3 years ago
6

Write the expression in terms of sin x and cos x only. sin(2x)+cos(3x)

Mathematics
2 answers:
BartSMP [9]3 years ago
5 0
Sin2x=2sinxcosx, cos2x=1-2sin^2x
sin(2x)+cos(3x)=2sinxcosx+cos(x+2x)
cos(x+2x)=cosx(1-2sin^2(x))-sinx2sinxcosx
sin(2x)+cos(3x)=2sinxcosx(1-sinx)+cosx(1-2sin^2(x))
Alisiya [41]3 years ago
5 0
Use the following identities:
\sin{2x}=2\sin{x}\cos{x}\\ \cos{2x}=\cos^2{x}-\sin^2{x} \\ \cos{(x+y)}=\cos{x}\cos{y}-\sin{x}\sin{y}

\sin{2x}+\cos{3x} \\=2\sin{x}\cos{x}+\cos{(2x+x)} \\=2\sin{x}\cos{x}+\cos{2x}\cos{x}-\sin{2x}\sin{x} \\=2\sin{x}\cos{x}+(\cos^2{x}-\sin^2{x})\cos{x}-2\sin{x}\cos{x}\sin{x} \\=2\sin{x}\cos{x}+\cos^3{x}-\sin^2{x}\cos{x}-2\sin^2{x}\cos{x} \\=2\sin{x}\cos{x}+\cos^3{x}-3\sin^2{x}\cos{x} 
\\=\sin{x}\cos{x}(2+\cos^2{x}-3\sin{x})


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Answer:

(k): 65k=c   is true  per kilometer he runs,

Step-by-step explanation:

(k): 65k=c   is true     if Yutaka was to walk and burn only 48 calories then k then is x= walk  and y = run   8x+7y>= c      8x+7y>=  8(48) + 7(65) >= 839

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Slav-nsk [51]

Triangle ABC is an isosceles triangle.

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Given data:

∠ABC = 70° and ∠ACD = 55°

<em>If two parallel lines are cut by a transversal, then alternate interior angles are congruent.</em>

m∠BAC = m∠ACD

m∠BAC = 55°

<em>Sum of the angles in a straight line add up to 180°.</em>

m∠ACD + m∠ACB + m∠ABC = 180°

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In triangle ABC,

∠BAC = 55° and ∠ACB = 55°

∠BAC = ∠ACB

Two angles in the triangle are equal.

Therefor triangle ABC is an isosceles triangle.

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Step-by-step explanation:

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Step-by-step explanation:
To find the answer we first have to find the value of each percent, to do this we divide 100 by 350, that gets us approximately 0.286. We know that he won 154 of them we then multiply 154 by 0.286 to get the percentage of games he won and we get 44.044.
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