<span>(1 + cos² 3θ) / (sin² 3θ) = 2 csc² 3θ - 1
Starting with the left: Note that cos²θ + </span><span>sin²θ = 1.
In the same way: </span><span>cos²3θ + <span>sin²3θ = 1
</span></span>Therefore cos²3θ = 1 - <span>sin²3θ
</span> From the top: (1 + cos² 3θ) = 1 + 1 - sin²3θ = 2 - <span>sin²3θ
</span>
(1 + cos² 3θ) / (sin² 3θ) = (<span>2 - sin²3θ) / (sin² 3θ) = 2/</span><span>sin² 3θ - </span><span>sin²3θ/</span>sin²3θ
= 2/<span>sin² 3θ - 1; But 1/</span><span>sinθ = csc</span><span>θ, Similarly </span>1/sin3θ = csc3θ
= 2 *(1/sin<span>3θ)² - 1</span>
= 2csc²3θ - 1. Therefore LHS = RHS. QED.
Answer: $250
Step-by-step explanation:
The computer reduces by half of its value every year. It is originally valued at $4,000 so the value in 4 years can be calculated by the formula:
= 4,000 * 0.5 ^ number of years
= 4,000 * 0.5⁴
= $250
Another method is to reduce by half every year:
First year = 4,000 / 2 = $2,000
Second year = 2,000 / 2 = $1,000
Third year = 1,000 / 2 = $500
Fourth year = 500 / 2 = $250
Answer:
<h2>

</h2>
Step-by-step explanation:
The probability of occurring the event A is
.
The probability to occur the event B is
.
It is also given that the events are independent that is they do not depends on each other.
So, the probability of occurring both the events simultaneously can be get by simply multiplying the probabilities of both the events.
Hence, the probability is
}[/tex] =
.