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S_A_V [24]
3 years ago
6

HELPP PLSSS!!! When factoring a number, you can use _[blank 1] as a shortcut. For example, you can tell if 5 is a factor of a nu

mber if _[blank 21- Match each blank with the option that correctly fills in that blank. blank 2 blank 1 .: it is even .: divisibility rules :: its last digit is 0 or 5 :: the sum of its digits is a multiple of 3 * long division guessing and checking​

Mathematics
1 answer:
Andru [333]3 years ago
3 0

Answer:

blank 1: divisibility rules

blank 2: its last digit is 0 or 5

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To prove :One plus cot square theta into tan theta by sec square theta = cot theta
pickupchik [31]

we are given

\frac{(1+cot^2(\theta))*tan(\theta)}{sec^2(\theta)} =cot(\theta)

We will simplify left side and make it equal to right side

Left side:

\frac{(1+cot^2(\theta))*tan(\theta)}{sec^2(\theta)}

we can use trigonometric identity

1+cot^2(\theta)=csc^2(\theta)

we can replace it

\frac{(csc^2(\theta))*tan(\theta)}{sec^2(\theta)}

we know that

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so, we can replace it

and we get

\frac{cos^2(\theta)tan(\theta)}{sin^2(\theta)}

now, we know that

tan =sin/cos

\frac{cos^2(\theta)*sin(\theta)}{sin^2(\theta)*cos(\theta)}

we can simplify it

and we get

\frac{cos(\theta)}{sin(\theta)}

we can also write it as

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Right Side:

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\frac{(1+cot^2(\theta))*tan(\theta)}{sec^2(\theta)} =cot(\theta)......Answer

6 0
3 years ago
Find the exact value of tan(x-y) if sin x=8/17 cosy = 3/5
jolli1 [7]

To solve the the question we proceed as follows:

From trigonometric laws

(cos x)^2+(sin x)^2=1

(cos x)^2+(sin x)^2=1

sin (x-y)=sin x sin y-sin y cos x

cos (x-y)=cos x cos y+sin x xin y

si  x=\frac{8}{17}

cos x=sqrt(1-(sin x)^2)=sqrt(1-64/289)=sqrt(\frac{225}{289} )=\frac{15}{17}

cos y=\frac{3}{5}

sin x= sqrt(1- (cos x)^2)= sqrt(1-\frac{9}{25} )=sqrt(\frac{16}{25} )=\frac{4}{5}

thus

tan (x-y)=[sin (x-y)]/[cos (x-y)]

=[sin x cos y-sin y cos x]/[cos x cos y+sin x sin y]

plugging in the values we obtain:

[8/17 *3/5-4/5*15/7]/[15/17*3/5+8/17*4/5]

simplifying

[24/85-60/85]/[45/85+32/85]

=-\frac{36}{77}

6 0
2 years ago
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