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VashaNatasha [74]
3 years ago
13

Can someone please help me?

Mathematics
2 answers:
qwelly [4]3 years ago
8 0
A ) sin x ( \frac{sinx}{cosx}*cosx- \frac{cosx}{sinx}+*cos x)= \\ sinx(sinx- \frac{cos^{2} x}{sin^{2} x})=
sin^{2}x-cos^{2} x=1-cos^{2}x-cos^{2} x= \\ 1-2cos^{2}x
b ) 1 +  \frac{1}{cos^{2} x} *sin^{2} x=1+ \frac{sin^{2} x}{cos^{2} x} = \\  \frac{cos {2} x+sin x^{2} x}{cos^{2} x} = \frac{1}{cos^{2} x} =sec^{2} x
c)\frac{sinx}{1-cosx} + \frac{sinx}{1+cosx}= \frac{sin x ( 1+cosx)+sinx(1-cosx)}{1-cos^{2} x} = \\  \frac{sinx+sinxcosx+sinx-sinxcosxx}{1-cos^{2}x }= \\  \frac{2sinx}{sin^{2} x}   =  \frac{2}{sinx}=2 csc x
d) -tan ^{2}x+sec ^{2}x=- \frac{sin ^{2} x}{cos ^{2} x} + \frac{1}{cos^{2} x} = \\  \frac{1-sin^{2x} }{cos ^{2}x }= \frac{cos^{2} x}{cos^{2}x }  =1
sattari [20]3 years ago
4 0

Answer:

a ) sin x ( \frac{sinx}{cosx}*cosx- \frac{cosx}{sinx}+*cos x)= \\ sinx(sinx- \frac{cos^{2} x}{sin^{2} x})=
sin^{2}x-cos^{2} x=1-cos^{2}x-cos^{2} x= \\ 1-2cos^{2}x    

b ) 1 +  \frac{1}{cos^{2} x} *sin^{2} x=1+ \frac{sin^{2} x}{cos^{2} x} = \\  \frac{cos {2} x+sin x^{2} x}{cos^{2} x} = \frac{1}{cos^{2} x} =sec^{2} x

c) \frac{sinx}{1-cosx} + \frac{sinx}{1+cosx}= \frac{sin x ( 1+cosx)+sinx(1-cosx)}{1-cos^{2} x} = \\  \frac{sinx+sinxcosx+sinx-sinxcosxx}{1-cos^{2}x }= \\  \frac{2sinx}{sin^{2} x}   =  \frac{2}{sinx}=2 csc x  

d) -tan ^{2}x+sec ^{2}x=- \frac{sin ^{2} x}{cos ^{2} x} + \frac{1}{cos^{2} x} = \\  \frac{1-sin^{2x} }{cos ^{2}x }= \frac{cos^{2} x}{cos^{2}x }  =1  

Step-by-step explanation:

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When Alice spends the day with the babysitter, there is a 0.6 probability that she turns on the TV and watches a show. Her littl
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Answer:

a) There is a 48% probability that both Alice and Betty watch TV tomorrow.

b) There is a 48% probability that Betty watches TV tomorrow.

c) There is a 12% probability that only Alice watches TV tomorrow.

Step-by-step explanation:

We have these following probabilities:

A 60% probability that Alice watches TV.

If Alice watches TV, an 80% probability Betty watches TV.

If Alice does not watch TV, a 0% probability that Betty watches TV, since she cannot turn the TV on by herself.

a) What is the probability that both Alice and Betty watch TV tomorrow?

Alice watches 60% of the time. Betty watches in 80% of the time Alice watches. So:

P = 0.6*0.8 = 0.48

There is a 48% probability that both Alice and Betty watch TV tomorrow.

b) What is the probability that Betty watches TV tomorrow?

Since Betty only watches when Alice watches(80% of the time), this probability is the same as the probability of both of them watching. So

P = 0.6*0.8 = 0.48

There is a 48% probability that Betty watches TV tomorrow.

c) What is the probability that only Alice watches TV tomorrow?

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There is a 12% probability that only Alice watches TV tomorrow.

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