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saveliy_v [14]
3 years ago
14

Prove that sinxtanx=1/cosx - cosx

Mathematics
1 answer:
maks197457 [2]3 years ago
5 0

Answer:

See below

Step-by-step explanation:

We want to prove that

\sin(x)\tan(x) = \dfrac{1}{\cos(x)} - \cos(x), \forall x \in\mathbb{R}

Taking the RHS, note

\dfrac{1}{\cos(x)} - \cos(x) = \dfrac{1}{\cos(x)} - \dfrac{\cos(x) \cos(x)}{\cos(x)} = \dfrac{1-\cos^2(x)}{\cos(x)}

Remember that

\sin^2(x) + \cos^2(x) =1 \implies 1- \cos^2(x) =\sin^2(x)

Therefore,

\dfrac{1-\cos^2(x)}{\cos(x)} = \dfrac{\sin^2(x)}{\cos(x)} = \dfrac{\sin(x)\sin(x)}{\cos(x)}

Once

\dfrac{\sin(x)}{\cos(x)} = \tan(x)

Then,

\dfrac{\sin(x)\sin(x)}{\cos(x)} = \sin(x)\tan(x)

Hence, it is proved

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Crank

Answer:

It snowed for 6 days in November

Step-by-step explanation:

Since there are 30 days in November

and 20 goes into 100 five times,

30/5=6, so in november snow fell for 6 days

5 0
3 years ago
Which equation represents the statement thirteen less then a number is forty two
Ludmilka [50]
X-13=42 
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3 0
3 years ago
Read 2 more answers
Solve the system by substitution.<br> 4y =<br> 5x -10y =-50
Trava [24]

Answer:

x = -20 ; y =-5

Step-by-step explanation:

Eqn. 1 ----> 4y = x

Eqn. 2 ----> 5x-10y = -50

(Simplifying eqn.2 further)

=>5(x-2y)=-50

=>x-2y=\frac{-50}{5} =-10

(Substituting the value of x from eqn. 1)

=>4y-2y=-10

=>2y=-10

=>y =\frac{-10}{2} =-5

Now, substituting the value of y in eqn. 1 ,

x = 4*(-5)=-20

7 0
2 years ago
Tyler can shovel the driveway in 2 hours Dakota can complete the job in 90 minutes if they work together how long will it take
topjm [15]
One JOB = 1  and 2 hours = 120 min

Tyler Rate per minute: 1/120 (in 1 minute he performes 1/120 of the job)
Dakota<span> Rate per minute: 1/90 (in 1 minute he performes 1/90 of the job)

Tyler's + Dakota's rate per 1 minute = 1/120 + 1/90  = 7/360 (Job/minutes)

7/360 of the job was performed in 1 minute
</span>a complete JOB =1 to be performed in x minutes (Rule of three)

x = 1x1/(7/360) that equals to 360/7 and x (time of both) = 51 min 42

5 0
3 years ago
PLEASE HELP!! ILL GIVE YOU BRAINLIEST!!
schepotkina [342]

Answer:

because when x ing a positive to a negative it will give you a negative however if you x a negative and a negitive it will give a positive

Step-by-step explanation:

7 0
3 years ago
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