(a) Given that sin y = \(\frac{8}{17}\) find the value of \(\frac{tan y}{1 + 2 tan y}\)
(b) An amount of N300,000.00 was shared among Otobo, Ada and Adeola. Otobo received N60,000.00, Ada received \(\frac{5}{10}\) of the remainder, while the rest went to Adeola. In what ratio was the money shared?
(a) Finding tan(y) using sin(y):
We cannot directly find the tangent (tan) of an angle using only the sine (sin). However, we can use the trigonometric identity:
tan^2(x) + 1 = sec^2(x)
where x is the angle and sec(x) is the secant (1/cos(x)).
Here's how to solve for tan(y):
- We are given sin(y) = 8/17. We cannot find cos(y) directly from this information.
- Since we cannot isolate tan(y) from the given identity, we cannot directly calculate its value.
Therefore, it's impossible to determine the value of
tan(y) + 2tan(y)/(1 + 2tan(y)) with the given information.
(b) Sharing Money:
Step 1: Calculate the remaining amount after Otobo's share.
Total money - Otobo's share
= N300,000.00 - N60,000.00 = N240,000.00
Step 2: Find Ada's share.
Ada receives 5/10 (which is the same as 1/2) of the remaining amount.
Ada's share = N240,000.00 * (1/2) = N120,000.00
Step 3: Calculate Adeola's share.
The remaining amount goes to Adeola.
Adeola's share = Total remaining - Ada's share
= N240,000.00 - N120,000.00 = N120,000.00
Step 4: Determine the ratio of shares.
Otobo : Ada : Adeola
= N60,000.00 : N120,000.00 : N120,000.00
Ratio: 3 : 6 : 6 (simplifying, 1 : 2 : 2)
Therefore, the money was shared in a ratio of 1 : 2 : 2 among Otobo, Ada, and Adeola respectively.