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BabaBlast [244]
3 years ago
5

How would you prove this trigonomic identity? Please show steps.

Mathematics
1 answer:
Agata [3.3K]3 years ago
4 0

Start by combining the fractions:

\dfrac{\cos\alpha}{1+\sin\alpha}\cdot\dfrac{1-\sin\alpha}{1-\sin\alpha}+\dfrac{\cos\alpha}{1-\sin\alpha}\cdot\dfrac{1+\sin\alpha}{1+\sin\alpha}

\dfrac{\cos\alpha(1-\sin\alpha)+\cos\alpha(1+\sin\alpha)}{(1+\sin\alpha)(1-\sin\alpha)}

\dfrac{2\cos\alpha}{1-\sin^2\alpha}

Recall the Pythagorean identity:

\dfrac{2\cos\alpha}{\cos^2\alpha}

Then cancel a factor of \cos\alpha and use the definition of secant:

\dfrac2{\cos\alpha}=\boxed{2\sec\alpha}

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Enter product in simplest form<br>1/4×7 4/5​
grigory [225]

Answer:

i believe the answer is 39/20 which could also be 13/7

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
The aspect ratio of a TV screen is the ratio of the width to the height of the image. A regular TV has an aspect ratio of 16: 9.
ki77a [65]

Answer:

Width = 44.45 inches

Height = 25.00 inches

Step-by-step explanation:

(16x)^2 + (9x)^2 = 51^2

256x^2 + 81x^2 = 2601

337x^2 = 2601

x^2 = 7.718

x = 2.778

Width = 44.45 inches

Height = 25.00 inches

I think this is right

7 0
3 years ago
What's the answer????
lana66690 [7]

Answer:

7

Step-by-step explanation:

2(3)(0) + 7

6(0) + 7

0 + 7

7

Have an amazing day!

<u><em>PLEASE RATE!</em></u>

8 0
2 years ago
What is the probability that a point chosen at random in the given figure will be inside the smaller square?
Aliun [14]
I have to interpret that:

1) the smaller square has side length = 3 cm

2) the bigger square has side length = 5 cm

3) the smaller square is completely inside the bigger square.

4) the points cannot be outside the bigger square



Under those assumptions the probability that a point is inside the smaller square  is

P (inside the smaller square) = area of the smaller square / area of the bigger square

P (inside the smaller squere) = (3cm)^2 / (5cm)^2 =  9 / 25


Answer: 9 / 25
8 0
3 years ago
Which is more 1/4 of rhe cheese pizza or 2/5 of the onion pizza
Leni [432]
Who eats onion pizza?

anyway, make bases same

1/4 times 5/5=5/20
2/5 times 4/4=8/20
5/20 vs 8/20
8/20 i bigger

2/5 is bigger

actaully depends on how big th pizza is
cheese could be 12 feet wide and the onion could be 12 inches wide
6 0
3 years ago
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