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KengaRu [80]
3 years ago
15

Prove. sin³A-cos³A/sinA-cosA = 1+sinAcosA​

Mathematics
1 answer:
katovenus [111]3 years ago
7 0

Answer:

\frac{ \sin {}^{3} A -  \cos {}^{3}  A }{ \sin A -  \cos A}  \\  \\ { \sf{ =  \frac{ {( \sin A -  \cos A)}^{3}   +  3 \sin A \cos A( \sin A  -   \cos A)}{ \sin A -  \cos A}  }} \\  \\  =  { {( \sin A -  \cos A)}^{2}  +  3 \sin A \cos A} \\ { \sf{ = ( \sin {}^{2}  A +  \cos {}^{2}  A) - 2 \sin  A \cos  A + 3\sin  A \cos  A}}  \\  = { \sf{1 +\sin  A \cos  A }}

#hence proved

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Use the formula to evaluate the series 1+2+4+8+...a10
valina [46]

Answer:

The sum of the given series is 1023

Step-by-step explanation:

Geometric series states that a series in which a constant ratio is obtained by multiplying the previous term.

Sum of the geometric series is given by:

S_n = \frac{a(1-r^n)}{1-r}

where a is the first term and n is the number of term.

Given the series: 1+2+4+8+.................+a_{10}

This is a geometric series with common ratio(r) = 2

We have to find the sum of the series for 10th term.

⇒ n = 10 and a = 1

then;

S_n = \frac{1(1-2^{10})}{1-2} =\frac{1-1024}{-1} =\frac{-1023}{-1}=1023

Therefore, the sum of the given series is 1023



8 0
3 years ago
Find the rate of change of the area of a square with respect
Romashka [77]
Let the side length of the square be x, then A = x^2
but diagonal (z) = sqrt(2x^2)
z^2 = 2x^2
x^2 = 1/2 z^2

Thus, A = 1/2 z^2
dA/dz = 1/2 (2z) = z
The rate of change is z.

When z = 4, the rate is 4.
4 0
3 years ago
What is 1/2 minus 1/4?
Oliga [24]

Answer:1/4

Step-by-step explanation:

1/2 is the same thing as 2/4 so.... 2/4 minus 1/4 is 1/4

3 0
3 years ago
Read 2 more answers
How can you represent an decrease in temperature using an addition equation? Explain!
kap26 [50]
Hm good question. Maybe you can measure the temperature in a place and measure another temperature in a other place and add it together.
6 0
3 years ago
Lori buys a $586 certificate of deposit (CD) that earns 6.6% interest that compounds monthly. How much will the CD be worth in 1
Alex777 [14]

Answer:

<h2>$1344.9</h2>

Step-by-step explanation:

This problem can be solved using the compound interest formula

A= P(1+r)^t

Given data

A, final amount =?

P, principal = $586

rate, r= 6.6% = 0.066

Time, t= 13 years

Substituting our values into the expression we have

A= 586(1+0.066)^1^3\\\ A= 586*(1.066)^13\\\ A= 586*2.295\\\ A= 1344.87

To the nearest cent the in 13 years the CD will be worth $1344.9

3 0
2 years ago
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