Which is equivalent to the equation y=3x+z/4

Show that sec(x)-tan(x)sin(x)=cos(x)is an identity for any value of x.

Dmitriy789 [7]

Here is one way to show that the left side is identical to the right side.

$\sec(x)-\tan(x)\sin(x) = \cos(x)\\\\\\\frac{1}{\cos(x)}-\frac{\sin(x)}{\cos(x)}\sin(x) = \cos(x)\\\\\\\frac{1}{\cos(x)}-\frac{\sin^2(x)}{\cos(x)} = \cos(x)\\\\\\\frac{1-\sin^2(x)}{\cos(x)} = \cos(x)\\\\\\\frac{\cos^2(x)}{\cos(x)} = \cos(x)\\\\\\\cos(x)=\cos(x)\\\\\\$

Throughout the entire process, the right hand side stayed the same. When working on identities, it's important to keep one side the same while you transform the other side.

Despite the two sides being identical when simplified, there is the issue of cos(x) being zero in the denominator on the left hand side. Be sure to account for this when forming the domain. No such issue occurs on the right hand side. For instance, the value x = pi/2 leads to a division by zero error when in radian mode. So if I was your teacher, I would revise the "for any value of x" and replace it with something along the lines of "for any x value in the domain".

3 0

3 years ago

The photographer got the baby to smile in 30% of the photos he took. If the baby smiled in 12 photos how many photos did the pho

slamgirl [31]

Answer:

40 photos

Step-by-step explanation:

$\frac{3}{10} =\frac{12}{y}$

3 × y = 12 × 10

3y = 120

y = 40

5 0

2 years ago

Complete the statement to describe the expression (a+b)(d+e)(a+b)(d+e)left parenthesis, a, plus, b, right parenthesis, left pare

UNO [17]

Answer:

The expression contains two factor and each factor contains 2 terms.

Step-by-step explanation:

We are given the expression:

$(a+b)(d+e)(a+b)(d+e) = (a+b)^2(d+e)^2$

A factor can be a number, variable, term, or a longer expression.
A factor is made of of terms and can be a constant, number or a variable.

Now, the expression contains two factor and each factor contains 2 terms.

The factors of expression are:

$1. ~(a+b)\\\text{This factor have a multiplicity of 2 in the expression.}\\2.~ (d+e)\\\text{This factor have a multiplicity of 2 in the expression.}$