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lubasha [3.4K]
2 years ago
11

Prove the following relations: 1) (1 - cos²A) (1 + tan²A) = tan²A​

Mathematics
1 answer:
JulsSmile [24]2 years ago
7 0

Step-by-step explanation:

(1 - cos²A)(1 + tan²A) = tan²A

1 + tan²A - cos²A - cos²A · tan²A = tan²A

1 + tan²A(1 - cos²A) - cos²A = tan²A

1 - cos²A + tan²A(sin²A) = tan²A

sin²A + tan²A(sin²A) = tan²A

sin²A (1 + tan²A) = tan²A

sin²A (sec²A) = tan²A

sin²A (1/cos²A) = tan²A

(sin²A)/(cos²A) = tan²A

tan²A = tan²A → <u>Proved</u>

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Answer:

a) 6.04661760*10^8

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Step-by-step explanation:

a)

There are 26 lowercase letters and 10 digits.  

The character that must be a digit can be generated in 10 different ways and the others, in 26+10=36 different ways.

Since the password is 6 characters long, by the Fundamental Rule of Counting there are

10*36*36*36*36*36 = 604,661,760

In scientific notation this number can be expressed as

6.04661760*10^8

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To get the denominators to be the same, we can...

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At this point, both fractions involve the denominator 48. We can add the fractions like so

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The last step is to reduce if possible. In this case, we can reduce. This is because 14 and 48 have the factor 2 in common. Divide each part by 2.

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The fraction 14/48 reduces to 7/24

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Step-by-step explanation:

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