MATHEMATICS HIGH SCHOOL

Prove that sin(x) + tan(x) = 1 + sec(x)/csc(x) by using trigonometric identities.

Answers

Answer 1

Answer:

Step-by-step explanation:

sin(x) + tan(x) =sin(X) + sin(x)/cos(x)

=sinx(1+1/cosx)

=Sinx(1+secx)

=1+secx/cosecx. (Since sinx=1/cosecx)

Hence LHS=RHS proved

Related Questions

Choose the correct simplification of the expression (3x − 6)(2x2 − 4x − 5).6x3 − 24x2 + 9x − 30 6x3 + 9x + 30 6x3 − 24x2 + 9x + 30 6x3 − 24x2 + 39x + 30
Arrange the systems of equations in order from least to greatest based on the number of solutions for each system.
Y=4x-7 make x the subject of the equation
PLEASE HELP ME WITH MY MATHS HOMEWORK BELOWif you answer it correctly i will rate you 5 stars and brainiest
The first one to answer gets ( a best answer )

Find the slope of the line that contains (4, -10) and
(3,9).

Answers

Answer:

The slope of the line is -19. A line that will pass through that will be y=-19x+66. THE ANSWER YOU ARE LOOKING FOR IS THAT THE SLOPE IS -19

Step-by-step explanation:

m = (y2 - y1)/(x2 - x1) [Formula to find slope from two points]

m=(9-(-10))/(3-4) [Plugging the two points in]

m= -19 [Answer]

Round to the given place: 256,035 (thousands)

Answers

So,

When rounding to the nearest thousand, look at the number in the hundreds place. If it is greater than or equal to 5, round up. If not, round down.

256,035

The hundreds place is less than 5, so we round down.

256,035 --> 256,000

256,000. The 6 is in the thousandths place, and since the 0 in the hundredths place is less than 5, you do not round up, keeping the 256,000 as opposed to 257,000.

Suppose you deposit $5,000 in a savings account that earns 3% annual interest. If you make no other withdrawals or deposits, how many years will it take the account balance to reach at least $6,000? A. 10 years. B. 6 years. C. 7 years. D. 4 years

Answers

You need to use the equation y=p(1+r)^t where p= the principle (initial amount), r= the rate of decay or growth, and t= the time. So y=5,000(1.03)^x is the equation you'd want to use. At 6 years you'd have $5,970.3 and at 7 $6,149.40, so the answer is C.

taking into consideration that the interest is compound (yearly)
the amount of money gather through the years can be calculated by

A = P (1+r)^(t)
6000 = 5000 (1.03)^t

t = ln(6000/5000)/ln(1.03) = 6.16 ≈ 7

c. 7 years

How many ways can the letters of the word ORGANISM be arranged so the third letter is G?

Answers

$7!=5040$
..........

Complete the equation of the graphed linear function in point-slope form.y – (–2) = ___(x – ___)

Answers

$m = (y_(2) - y_(1))/(x_(2) - x_(1)) = (2 - (-2))/(2 - 1) = (2 + 2)/(1) = (4)/(1) = 4$

y - y₁ = m(x - x₁)
y - (-2) = 4(x - 1)
y + 2 = 4(x - 1)
y + 2 = 4(x) - 4(1)
y + 2 = 4x - 4
- 2 - 2
y = 4x - 6

Jade invested $13,500 at 5.2% interest, compounded semiannually, and she wants to know how much her investment will be worth in 8 years
Part 1: What is the periodic interest rate of jade investment
Part 2: How many compounding periods does jades investment offer in a year? how about in 8 years?

Answers

Part 1: What is the periodic interest rate of jade investment?

Each compounding period is done semi-annually, which means twice a year. Since the given interest rate is annual, then 5.2% divided by half should yield the period interest rate, which is 2.6%

Part 2: How many compounding periods does Jade's investment offer in a year? how about in 8 years?

In 1 year, there are 2 compounding periods. In 2 years, there are 16 compounding periods.

Answer:

Part 3: What expression can Jade write to figure out how much her investment will be worth in 8 years? F = $13,500.00 * (1 + .052/2) ^ (2*8)

Part 4: How much will Jade's investment be worth in 8 years? $20,355.96

Step-by-step explanation:

Other Questions

One number is 1 more than 4 times another. Their product is 18. What are the numbers?

Simplify (1/81) to the 1/4 power

Can i know the steps to this answer?

Challenge The price of Stock A at 9 am was $14.11. Since then the price has been increasing atthe rate of $0.08 each hour. At noon the price of Stock B was $14.86. It begins to decrease at therate of $0.14 each hour. If the two rates continue, in how many hours will the prices of the baostocks be the same?In about