The answer is 47 no I don’t want thank you
Expanded FormExpanded form refers to a base and an exponent written as repeated multiplication. ExponentExponents are used to describe the number of times that a term is multiplied by itself. ExpressionAn expression is a mathematical phrase containing variables, operations and/or numbers.
Answer:
2sin²θ - tan²θ
Step-by-step explanation:
Given
tan²θcos(2θ)
Required
Simplify
We start by simplifying cos(2θ)
cos(2θ) = cos(θ+θ)
From Cosine formula
cos(A+A) = cosAcosA - sinAsinA
cos(A+A) = cos²A - sin²A
By comparison
cos(2θ) = cos(θ+θ)
cos(2θ) = cos²θ - sin²θ ----- equation 1
Recall that cos²θ + sin²θ = 1
Make sin²θ the subject of formula
sin²θ = 1 - cos²θ
Substitute sin²θ = 1 - cos²θ in equation 1
cos(2θ) = cos²θ - (1 - cos²θ)
cos(2θ) = cos²θ - 1 +cos²θ
cos(2θ) = cos²θ + cos²θ - 1
cos(2θ) = 2cos²θ - 1
Substitute 2cos²θ - 1 for cos(2θ) in the given question
tan²θcos(2θ) becomes
tan²θ(2cos²θ - 1)
Open brackets
2cos²θtan²θ - tan²θ
------------------------
Simplify tan²θ
tan²θ = (tanθ)²
Recall that tanθ = sinθ/cosθ
So, we have
tan²θ = (sinθ/cosθ)²
tan²θ = sin²θ/cos²θ
------------------------
Substitute sin²θ/cos²θ for tan²θ
2cos²θtan²θ - tan²θ becomes
2cos²θ(sin²θ/cos²θ) - tan²θ
Open bracket (cos²θ will cancel out cos²θ) to give
2(sin²θ) - tan²θ
2sin²θ - tan²θ
Hence, the simplification of tan²θcos(2θ) is 2sin²θ - tan²θ
Option E is correct
In order to reduce ANY fraction to lowest terms, find any common factors
of the numerator and denominator, and divide them both by it. If they still
have a common factor, then divide them by it again. Eventually, they won't
have any common factor except ' 1 ', and then you'll know that the fraction is
in lowest terms.
Do 15 and 40 have any common factors ?
Let's see . . .
The factors of 15 are 1, 3, <em>5</em>, and 15 .
The factors of 40 are 1, 2, 4,<em> 5</em>, 8, 10, 20, and 40 .
Ah hah ! Do you see that ' <em>5</em> ' on both lists ? That's a common factor.
So 15/40 is NOT in lowest terms.
Divide the numerator and denominator both by 5 :
15 / 40 =<em> 3 / 8</em>
3 and 8 don't have any common factor except ' 1 '.
So 3/8 is the same number as 15/40, but in lowest terms.
1 square inch = 2.54^2 = 6.4516 square cms
So 5.60 in^2 = 6.60 * 6.4516 = 36.13cm^2 to nearest hundredth
