All categories

3 years ago

Prove the identity

Mathematics

1 answer:

Troyanec [42]3 years ago

3 0

Answer:

Proved

Step-by-step explanation:

The options are not given. So, I will solve from scratch

Given

$\frac{secx-1}{tan x}= \frac{tanx}{secx+1}$

Required

Prove

Multiply the right-hand side by $\frac{secx + 1}{secx + 1}$

$\frac{secx-1}{tan x} * \frac{secx + 1}{secx + 1}= \frac{tanx}{secx+1}$

Apply difference of two squares on the numerator

$\frac{sec^2 x - 1}{(tanx)(secx + 1)} =\frac{tanx}{secx+1}$

In trigonometry:

$tan^2x = sec^2x - 1$

So, we have:

$\frac{tan^2 x}{(tanx)(secx + 1)} =\frac{tanx}{secx+1}$

$\frac{tan x * tan x}{(tanx)(secx + 1)} =\frac{tanx}{secx+1}$

tan x cancels out

$\frac{tan x}{secx + 1} =\frac{tanx}{secx+1}$

Proved

You might be interested in

You have a coupon for $5 off your total bill at Mama's Meals on Main a. How much will you pay after using the coupon if your bil

HACTEHA [7]

Answer :

(a) Amount paid after using the coupon = $b - $5 = $(b-5)

(b) Amount paid = $23.45 - $5 = $(23.45-5) = $18.45

Amount paid = $54.83- $5 = $(54.83-5) = $49.83

Step-by-step explanation :

As we are given that:

Amount of coupon = $5

If amount of total bill = $b

Now we have to calculate the amount paid after using the coupon.

Amount paid after using the coupon = Total amount of bill - Amount of coupon

Amount paid after using the coupon = $b - $5 = $(b-5)

Now we have to calculate the amount paid if bill was $23.45.

Amount paid after using the coupon = Total amount of bill - Amount of coupon

Amount paid = $23.45 - $5 = $(23.45-5) = $18.45

Now we have to calculate the amount paid if bill was $54.83.

Amount paid after using the coupon = Total amount of bill - Amount of coupon

Amount paid = $54.83- $5 = $(54.83-5) = $49.83

6 0

3 years ago

Factor completely x_ - 36. (1 point) (x + 6)(x - 6) (X+6)(x+6) (X-6)(x - 6) Prime

Andrews [41]

Answer:

Step-by-step explanation:

6 0

3 years ago

The students in a class and the teacher visited a park on a field trip. The students were taught how to plant seeds, and the tea

drek231 [11]

The answer is B because the teacher is keeping count of the seeds that EACH student plants

6 0

3 years ago

Read 2 more answers

How do you concert percent into fractions in simple form

Rasek [7]

You have to convert the percent into a decimal before you convert it into a fraction then you simplify the fraction.
Hope this helps! :)

5 0

3 years ago

What is the probability that a randomly selected graduate has a job if he or she is attending college? Give your answer as

Andrej [43]

Complete question :

Suppose that of the 300 seniors who graduated from Schwarzchild High School last spring, some have jobs, some are attending college, and some are doing both. The following Venn diagram shows the number of graduates in each category. What is the probability that a randomly selected graduate has a job if he or she is attending college? Give your answer as a decimal precise to two decimal places.

What is the probability that a randomly selected graduate attends college if he or she has a job? Give your answer as a decimal precise to two decimal places.

Answer:

0.56 ; 0.60

Step-by-step explanation:

From The attached Venn diagram :

C = attend college ; J = has a job

P(C) = (35+45)/300 = 80/300 = 8/30

P(J) = (30+45)/300 = 75/300 = 0.25

P(C n J) = 45 /300 = 0.15

1.)

P(J | C) = P(C n J) / P(C)

P(J | C) = 0.15 / (8/30)

P(J | C) = 0.5625 = 0.56

2.)

P(C | J) = P(C n J) / P(J)

P(C | J) = 0.15 / (0.25)

P(C | J) = 0.6 = 0.60

5 0

3 years ago