How do you do these? I'm not sure on how to solve these and what to do to solve them.
1 answer:
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Answer:
or
.
Step-by-step explanation:
How are tangents and secants related to sines and cosines?
.
.
Sticking to either cosine or sine might help simplify the calculation. By the Pythagorean Theorem, . Therefore, for the square of tangents,
.
This equation will thus become:
.
To simplify the calculations, replace all with another variable. For example, let
. Keep in mind that
.
.
.
Solve this equation for :
.
.
.
Given that ,
is the only possible solution.
,
, where
(i.e.,
is an integer.)
Given that ,
.
or
. Accordingly,
or
.
Answer:
The value of n is 10
Step-by-step explanation:
The formula of the nth term of the arithmetic progression is a = a + (n - 1)d
- a is the first term
- d is the common difference between each 2 consecutive terms
- n is the position of the term
The formula of the sum of nth terms is S =
[2a + (n - 1)d]
∵ An AP has a common difference of 3
∴ d = 3
∵ The nth term is 32
∴ a = 32
→ Substitute them in the 1st rule above
∵ 32 = a + (n - 1)3
∴ 32 = a + 3(n) - 3(1)
∴ 32 = a + 3n - 3
→ Add 3 to both sides
∴ 35 = a + 3n
→ Switch the two sides
∴ a + 3n = 35
→ Subtract 3n from both sides
∴ a = 35 - 3n ⇒ (1)
∵ The sum of the first n terms is 185
∴ S = 185
→ Substitute the value of S and d in the 2nd rule above
∵ 185 = [ 2a + (n - 1)3]
∴ 185 = [2a + 3(n) - 3(1)]
∴ 185 = [2a + 3n - 3]
→ Multiply both sides by 2
∴ 370 = n(2a + 3n - 3)
∴ 370 = 2an + 3n² - 3n
→ Substitute a by equation (1)
∴ 370 = 2n(35 - 3n) + 3n² - 3n
∴ 370 = 70n - 6n²+ 3n² - 3n
→ Add the like terms in the right side
∵ 370 = -3n² + 67n
→ Add 3n² to both sides
∴ 3n² + 370 = 67n
→ Subtract 67 from both sides
∴ 3n² - 67n + 370 = 0
→ Use your calculator to find n
∴ n = 10 and n = 37/3
∵ n must be a positive integer ⇒ 37/3 neglecting
∴ n = 10
∴ The value of n is 10