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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

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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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

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

$=-\frac{36}{77}$

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2 years ago