Prove that sinA-sin3A+sin5A-sin7A/cosA-cos3A-cos5A+cos7A= cot2A

1 answer:

4 0

Write the left side of the given expression as N/D, where
N = sinA - sin3A + sin5A - sin7A
D = cosA - cos3A - cos5A + cos7A
Therefore we want to show that N/D = cot2A.

We shall use these identities:
sin x - sin y = 2cos((x+y)/2)*sin((x-y)/2)
cos x - cos y = -2sin((x+y)/2)*sin((x-y)2)

N = -(sin7A - sinA) + sin5A - sin3A
= -2cos4A*sin3A + 2cos4A*sinA
= 2cos4A(sinA - sin3A)
= 2cos4A*2cos(2A)sin(-A)
= -4cos4A*cos2A*sinA

D = cos7A + cosA - (cos5A + cos3A)
= 2cos4A*cos3A - 2cos4A*cosA
= 2cos4A(cos3A - cosA)
= 2cos4A*(-2)sin2A*sinA
= -4cos4A*sin2A*sinA

Therefore
N/D = [-4cos4A*cos2A*sinA]/[-4cos4A*sin2A*sinA]
= cos2A/sin2A
= cot2A

This verifies the identity.

You might be interested in

Jason is cutting a roll of sausage into pieces that are 1/2 inches thifk if the roll is 6 inchew long how many pieces of sausage

e-lub [12.9K]

Answer:

12 rolls

Step-by-step explanation:

Jason wants to cut roll into pieces that are each 1/2 inches thick. 1/2 is equal to 0.5, so thickness of each roll is 0.5 inches

Total length of the roll is 6 inches. We have to find how many small 0.5 inch rolls can he cut.

In simple words we can say that we have to find: how many 0.5 inches can be out from 6 inches. This type of problem is solved by division. Dividing 6 inches by 0.5 inches will give us: How many 0.5 inches can be cut out from 6 inches i.e. how many 0.5 inches roll can be made from 6 inches roll

6 divided by 0.5 is 12.

This means Jason can cut 12 rolls of sausages each with thickness of 0.5 inches from a roll of 6 inches.

7 0

3 years ago

The rational number that expresses a loss of $25.30 is +$25.30 -$25.30 +$2.53 -$2.53 , and the rational number that represents a

Mkey [24]

It’s the 2nd one I hope this helps homie

7 0

3 years ago

Read 2 more answers

Consider the expression 2√3 cos(x)csc(x)+4cos(x)-3csc(x)-2 √ 3 This expression can be represented as the product of the factors.

Alla [95]

Answer with explanation:

The given expression is:

$2 \sqrt{3}\cos x * \csc x+4 \cos x-3 \csc x-2\sqrt{3}\\\\=2 \cos x*(\sqrt{3}*\csc x+2)-\sqrt{3}*(\sqrt{3}*\csc x+2)\\\\\rightarrow (2\cos x -\sqrt{3})*(\sqrt{3}*\csc x+2)\\\\\rightarrow (2\cos x -\sqrt{3})*(\sqrt{3}*\csc x+2)=0\\\\(2\cos x -\sqrt{3})=0 \wedge (\sqrt{3}*\csc x+2)=0$

$\cos x=\frac{\sqrt{3}}{2} \wedge \csc x=\frac{-2}{\sqrt{3}}\\\\x=\frac{\pi}{6},2\pi-\frac{\pi}{6}\\\\x=\frac{\pi}{6},\frac{11\pi}{6} \wedge x=\pi+\frac{\pi}{3} ,2\pi-\frac{\pi}{3}\\\\x=\frac{4\pi}{3},\frac{5\pi}{3}\\\\x={\frac{\pi}{6},\frac{11\pi}{6},\frac{4\pi}{3},\frac{5\pi}{3}}$

Option C

8 0

3 years ago

(Picture provided)<br><br> Helppppppp plsss

denpristay [2]

Answer:

100 degrees

Step-by-step explanation:

at first i thought it was a right angle but i looked at the other shape and seen it was a 80 degree angle for B, then i seen C on the same shape, so that just proved what i thought that W was on the other shape because its not a 90 degree right angle, its a bigger angle not as big as C on the other shape, but not a 90 degree angle either, so its 100 degree angle.

3 0

2 years ago

What is bigger 0.75 or 1 3/4

Simora [160]

1 3/4 is greater than 0.75 because 1 3/4 is 1.75 and it is greater than 0.75

5 0

3 years ago