Guidelines
Complete this statement: Two functions f(x) and g(x) are identically equal if f(x) = g(x) for any real number x \in mathbb R for ...
What is "which both functions are defined"?
This ratio in terms of sines and cosines is the same as tan(theta)
What is
sin(theta)/cos(theta)?
The first step to establish the identity:
cot(x)/csc(x) = cos(x)
What is rewrite left side in terms of sines and cosines?
csc(x) cdot cos(x) = tan(x)
What is no?
The trigonometric substitution for x that makes x/sqrt(1-x^2) equal to tan(x) for 0 < theta < pi/2
What is
x=sin(theta)?
True or False: When proving identities, it is common to change any trigonometric function to its sine or cosine equivalent.
What is True?
The reciprocal of cosine.
What is secant?
The first step in establishing the identity
csc(x) cdot tan(x) = sec(x)
What is rewrite the left side in terms of sines and cosines?
sec(x) \cdot sin(x) = tan(x)
What is yes?
The trigonometric substitution x=tan(theta) for 0 < theta < pi/2 makes sqrt(1+x^2) simplify to this.
What is
sec(x)?
Complete the statement: It is common to begin proving an identity with the side that is ...
What is "more complicated"?
The two trigonometric functions that are even functions.
What are cosine and secant?
The first step in establishing the identity
sin^2(-x) + cos^2(-x) = 1
What is use the even-odd properties?
cos(x)(tan(x) + cot(x)) = csc(x)
What is yes?
The trigonometric substitution that makes sqrt(x^2 - 1) simplify to tan(theta) for 0 < theta < pi/2 .
What is
x=sec(theta)?
What is False?
If we know sin^2(theta) + cos^2(theta) = 1 , obtain tan^2(theta) + 1 = sec^2(theta) by doing this.
What is divide both sides by the square of the cosine?
The first step in establishing the identity
sin(x)/(1+cos(x)) + (1+cos(x))/sin(x) = 2csc(x)
What is add the fractions on the left side?
tan(u)cot(u) - cos^2(u) = sin(u)
What is no?
If we have sqrt(9-x^2) and we substitute x = 3sin(theta) for 0 < theta < pi/2 , the expression simplifies to this.
What is
3cos(theta)?
True or False: Cross Multiplying is permitted when proving trigonometric identities
What is False?
ln|sec(x) + tan(x)| + ln|sec(x) - tan(x)| =
What is zero?
The first step in establishing the identity
(1-sin(x))/cos(x) = cos(x)/(1+sin(x))
What is multiply the numerator and denominator on the left side by
1+sin(x)?
3sin^2(x) + 4cos^2(x) = 3 - cos^2(x)
What is no?
If we have sqrt(x^2 - 25)/x and we make the trigonometric substitution x = 5 sec(theta) for 0 < theta < pi/2 , the expression simplifies to this.
What is
cos(theta)?