iii) (cosx-cosy)+ (sinx -siny)2 = 4cog2 (x + y)
2
Answers
Answer:
ANSWER EXPLANATION: There are two ways to solve this question. The faster way is to multiply each side of the given equation by ax−2 (so you can get rid of the fraction). When you multiply each side by ax−2, you should have:
24x2+25x−47=(−8x−3)(ax−2)−53
You should then multiply (−8x−3) and (ax−2) using FOIL.
24x2+25x−47=−8ax2−3ax+16x+6−53
Then, reduce on the right side of the equation
24x2+25x−47=−8ax2−3ax+16x−47
Since the coefficients of the x2-term have to be equal on both sides of the equation, −8a=24, or a=−3.
The other option which is longer and more tedious is to attempt to plug in all of the answer choices for a and see which answer choice makes both sides of the equation equal. Again, this is the longer option, and
Answer:
aare
Step-by-step explanation:
Trigonometric Functions of Acute Angles
sin X = opp / hyp = a / c , csc X = hyp / opp = c / a
tan X = opp / adj = a / b , cot X = adj / opp = b / a
cos X = adj / hyp = b / c , sec X = hyp / adj = c / b ,
acute angle trigonometric functions.
Trigonometric Functions of Arbitrary Angles
sin X = b / r , csc X = r / b
tan X = b / a , cot X = a / b
cos X = a / r , sec X = r / a
acute angle trigonometric functions.
Special Triangles
Special triangles may be used to find trigonometric functions of special angles: 30, 45 and 60 degress.
special triangles.
Sine and Cosine Laws in Triangles
In any triangle we have:
1 - The sine law
sin A / a = sin B / b = sin C / c
2 - The cosine laws
a 2 = b 2 + c 2 - 2 b c cos A
b 2 = a 2 + c 2 - 2 a c cos B
c 2 = a 2 + b 2 - 2 a b cos C
triangles.
Relations Between Trigonometric Functions
cscX = 1 / sinX
sinX = 1 / cscX
secX = 1 / cosX
cosX = 1 / secX
tanX = 1 / cotX
cotX = 1 / tanX
tanX = sinX / cosX
cotX = cosX / sinX
Pythagorean Identities
sin 2X + cos 2X = 1
1 + tan 2X = sec 2X
1 + cot 2X = csc 2X
Negative Angle Identities
sin(-X) = - sinX , odd function
csc(-X) = - cscX , odd function
cos(-X) = cosX , even function
sec(-X) = secX , even function
tan(-X) = - tanX , odd function
cot(-X) = - cotX , odd function
Cofunctions Identities
sin(π/2 - X) = cosX
cos(π/2 - X) = sinX
tan(π/2 - X) = cotX
cot(π/2 - X) = tanX
sec(π/2 - X) = cscX
csc(π/2 - X) = secX
Addition Formulas
cos(X + Y) = cosX cosY - sinX sinY
cos(X - Y) = cosX cosY + sinX sinY
sin(X + Y) = sinX cosY + cosX sinY
sin(X - Y) = sinX cosY - cosX sinY
tan(X + Y) = [ tanX + tanY ] / [ 1 - tanX tanY]
tan(X - Y) = [ tanX - tanY ] / [ 1 + tanX tanY]
cot(X + Y) = [ cotX cotY - 1 ] / [ cotX + cotY]
cot(X - Y) = [ cotX cotY + 1 ] / [ cotY - cotX]
Sum to Product Formulas
cosX + cosY = 2cos[ (X + Y) / 2 ] cos[ (X - Y) / 2 ]
sinX + sinY = 2sin[ (X + Y) / 2 ] cos[ (X - Y) / 2 ]
Difference to Product Formulas