If, A+B+C=π(i) Prove that, SinA+SinB-SinC = 4SinA/2. SinB/2. CosC/2
(ii) Prove that, Cos^2A + Cos^2B-Cos^2C = 1-2SinA.SinB.Cos.C
(iii) Prove that, CosA+CosB-CosC = -1+4CosA/2. CosB/2.SinC/2

Answers

Answer 1

Answer: (i)
A+B+C = pi
B+C = pi-A
sin(B+C) = sin(pi-A)
sin(B)cos(C)+cos(B)sin(C) = sin(pi)cos(A)-cos(pi)sin(A)
sin(B)cos(C)+cos(B)sin(C) = sin(A)
sin(B)cos(C) - sin(A) = -cos(B)sin(C)
(sin(B)cos(C) - sin(A))^2 = (-cos(B)sin(C))^2
sin^2(B)cos^2(C) + sin^2(A) - 2sin(A)sin(B)cos(C) = cos^2(B)sin^2(C)
-2sin(A)sin(B)cos(C) = cos^2(B)sin^2(C) - sin^2(B)cos^2(C) - sin^2(A)

(ii)
cos^2(A) + cos^2(B) - cos^2(C) = 1-2*sin(A)*sin(B)*cos(C)
cos^2(A) + cos^2(B) - cos^2(C) = 1+cos^2(B)sin^2(C) - sin^2(B)cos^2(C) - sin^2(A)
cos^2(A) + cos^2(B) - cos^2(C) = 1+(cos^2(B)sin^2(C) - sin^2(B)cos^2(C)) - sin^2(A)cos^2(A) + cos^2(B) - cos^2(C) = 1+((cos(B)sin(C))^2 - (sin(B)cos(C))^2) - sin^2(A)
cos^2(A) + cos^2(B) - cos^2(C) = 1+(cos(B)sin(C)-sin(B)cos(C))(cos(B)sin(C)+sin(B)cos(C)) - sin^2(A)
cos^2(A) + cos^2(B) - cos^2(C) = 1+(sin(C)cos(B)-cos(C)sin(B))(sin(C)cos(B)+cos(C)sin(B)) - sin^2(A)
cos^2(A) + cos^2(B) - cos^2(C) = 1+sin(C-B)sin(C+B) - sin^2(A)
cos^2(A) + cos^2(B) - cos^2(C) = 1+(1/2)*(cos(2B)-cos(2C)) - sin^2(A)
cos^2(A) + cos^2(B) - cos^2(C) = 1+(1/2)*(2cos^2(B)-1-(2cos^2(C)-1)) - sin^2(A)
cos^2(A) + cos^2(B) - cos^2(C) = 1+(1/2)*(2cos^2(B)-1-2cos^2(C)+1) - sin^2(A)
cos^2(A) + cos^2(B) - cos^2(C) = 1+(1/2)*(2cos^2(B)-2cos^2(C)) - sin^2(A)
cos^2(A) + cos^2(B) - cos^2(C) = 1+cos^2(B)-cos^2(C) - sin^2(A)
cos^2(A) + cos^2(B) - cos^2(C) = 1 - sin^2(A) + cos^2(B) - cos^2(C)
cos^2(A) + cos^2(B) - cos^2(C) = cos^2(A) + cos^2(B) - cos^2(C)

Related Questions

All rectangles are _____. A. rhombuses B. quadrilaterals C. parallelograms D. squares
Taylor cuts 1/5 sheet of construction paper. What fraction is equivalent to 1/5 ?1/6 3/15 15/45 15/3
An exponential function, f (x), is graphed on the coordinate plane. What is the equation for the function?A. f(x)=2(3)^xB. f(x)=4(2)^xC. f(x)=3(2)^xD. f(x)=3(4)^x
5y(2y-3)=(2y-3) can someone help me and explain step by step on how to do it
Write this polynomial in standard form:8x² - 4x³ + 12 - 5xoptions:(1.) 4x³ + 8x² - 5x + 12(2.) -4x³ + 8x² - 5x + 12(3.) 12 - 5x + 8x² - 4x³(12.) - 4x³ + 8x² - 5x

A cylindrical well is 20 meters deep and has a diameter of 1.5 meters. Approximately how many cubic meters of soil were dug out to make the well? (Use π = 3.14.)11.78 cubic meters
35.33 cubic meters
121.20 cubic meters
141.30 cubic meters

Answers

V = πr2h

V = 3.14 x 0.75 x 0.75 x 20

V = 35.33 cubic meters

Hope i will become the brainilest.

Answer:

35.33 cubic meters

Step-by-step explanation:

just took the test

Help it’s due today !!!

Answers

I believe it’s (A)
Because when u square root -3 it equals 9 when added to 5 gives u 14 and the rest don’t

Which of the following functions has the largest value when x = 3? (1 point)c(x) = 3x2 + 5x + 22
j(x) = 12x
a(x) = 9x

All the functions are equal at x = 3.
c(x)
j(x)
a(x)

Answers

x = 3

c(x) = 3x² + 5x + 22
⇒ c(3) = 3(3²) + 5(3) + 22
⇒ c(3) = 3(9) + 15 + 22
⇒ c(3) = 27 + 15 + 22
⇒ c(3) = 64

j(x) = 12x
⇒ j(3) = 12(3)
⇒ j(3) = 36

a(x) = 9x
⇒ a(3) = 9(3)
⇒ a(3) = 27

c(x) = 3x² + 5x + 22 is the function that has the largest value when x = 3.

False. Not all functions are equal at x = 3.

Answer: a(x) = $9^(x)$

An easy way to find this is by going on a graphing website like desmos. You simply put all of the equations into desmos and it will automatically recognize them as exponential functions, quadratic functions, etc. Once you do this you can write out x = 3 to create a line to compare them all.

If you can't use a graphing site, then simply insert 3 for x in each equation.

c(x) = 3 $(3)^(2)$ + 5(3) + 22

27 + 15 + 22 = 64

j(x) = 12(3)

12 * 3 = 36

a(x) = $9^((3))$

9 * 9 * 9 or 9^3 = 729

c(x) = 64

j(x) = 36

a(x) = 729

Find The Slope
(-4, 6) and (-2,1)

Answers

Answer:

-5/-6

Step-by-step explanation:

Use the equation rise over run, which is also y2-y1 over x2-x1

in basically every type of thing, x always comes first then y

y2=1 y1=6 x2=-2 x1=-4

1-6/-2-(-4)=-5/-6, because it was changed to, -5/-2+4

Victor Malaba has a net income of $1,240 per month. If he spends $150 on food, $244 on a carpayment, $300 on rent, and $50 on savings, what percent of his net income can he spend on other things
I'm getting lost when solving for x
Any help is greatly appreciated