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bixtya [17]
3 years ago
15

Please help me to prove this..​

Mathematics
2 answers:
kvasek [131]3 years ago
8 0

Answer:

hope it helps

plz mark brainliest✌️✌️

olya-2409 [2.1K]3 years ago
8 0

Answer:  see proof below

<u>Step-by-step explanation:</u>

Use the following Sum to Product Identities:

\sin x+\sin y=2\sin\bigg(\dfrac{x+y}{2}\bigg)\cos \bigg(\dfrac{x-y}{2}\bigg)\\\\\\\cos x-\cos y=-2\sin\bigg(\dfrac{x+y}{2}\bigg)\sin \bigg(\dfrac{x-y}{2}\bigg)

<u>Proof LHS →  RHS</u>

\text{LHS:}\qquad \qquad \qquad \qquad \dfrac{\sin \theta-\sin 3\theta+\sin 5\theta -\sin 7\theta}{\cos \theta -\cos 3\theta -\cos 5\theta +\cos 7\theta}

\text{Regroup:}\qquad \qquad \qquad \dfrac{(\sin 5\theta+\sin \theta)-(\sin 7\theta +\sin 3\theta)}{-(\cos 5\theta -\cos \theta) +(\cos 7\theta -\cos 3\theta)}

\text{Sum to Product:}\quad \dfrac{2\sin\bigg(\dfrac{5\theta +\theta}{2}\bigg)\cos \bigg(\dfrac{5\theta -\theta}{2}\bigg)-2\sin \bigg(\dfrac{7\theta + 3\theta}{2}\bigg)\cos \bigg(\dfrac{7\theta - 3\theta}{2}\bigg)}{2\sin\bigg(\dfrac{5\theta +\theta}{2}\bigg)\sin \bigg(\dfrac{5\theta -\theta}{2}\bigg)-2\sin \bigg(\dfrac{7\theta + 3\theta}{2}\bigg)\sin \bigg(\dfrac{7\theta - 3\theta}{2}\bigg)}

\text{Simplify:}\qquad \qquad \dfrac{2\sin 3\theta \cos 2\theta-2\sin 5\theta \cos 2\theta}{2\sin 3\theta \sin 2\theta-2\sin 5\theta \cos 2\theta}

\text{Factor:}\qquad \qquad \dfrac{\cos 2\theta(2\sin 3\theta -2\sin 5\theta \cos 2\theta)}{\sin 2\theta(2\sin 3\theta -2\sin 5\theta \cos 2\theta)}

\text{Simplify:}\qquad \qquad \dfrac{\cos 2\theta}{\sin 2\theta}\\\\.\qquad \qquad \qquad =\cot 2\theta

LHS = RHS:  cot 2Ф = cot 2Ф   \checkmark

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Trigonometric identities Simplify cos^2 theta -1/ 4 sin^2 theta
Veronika [31]

Answer:

B

Step-by-step explanation:

using the identity

sin²x + cos²x = 1 ( subtract 1 from both sides )

sin²x + cos²x - 1 = 0 ( subtract sin²x from both sides )

cos²x - 1 = - sin²x

then

\frac{cos^20-1}{4sin^20}

= \frac{-sin^20}{4sin^20} ← cancel sin²Θ on numerator and denominator

= \frac{-1}{4}

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4 0
2 years ago
The teacher asks Mel and Kate to use base 10 blocks to model the number that is ten times the value of 4 rods. Mel's modle uses
AveGali [126]
Kate's model is correct because 10 times the value of 4 rods, 10(4(10)), is 400. Mel's model represents 4(1)=4, which is incorrect. Kate's model represents 4*100=400, which is correct.
Hope I answered your question!
4 0
2 years ago
The quotient of 3 times a number and 7 is 15. Find the number<br> pls help me
Ronch [10]

Answer:

it would be 3 times 35 divded by 7 and that answer would give you 15 as the answer so 35 is your missing number

Step-by-step explanation:

4 0
3 years ago
If triangle ABC is isosceles and triangle DBE is equilateral what is the measure of angle C
luda_lava [24]

Answer:

43°

Step-by-step explanation:

For triangle ABC:

A = C so all we need to do is to calculate the value of B

The measure of angle ABD is given as 17° so the measure of angle EBC must be 17° as well

Since DBE is an equilateral triangle angle is DBE = 60°

17 + 17 + 60 = 94 this is the measure of angle B

The sum of interior angles in a triangle is equal to 180

A + B + C = 180

A + C + 94 = 180

A + C = 86 since A = C we divide 86 by 2

C = 43°

6 0
2 years ago
✨✨ Easy points for those who are good at math! ✨✨
GuDViN [60]
Is it option two hope I got it
7 0
2 years ago
Read 2 more answers
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