Without using trignometery tables find value of , cos70/sin20+cos57.cosec33 - 2cos60

1 answer:

4 0

Here is some thoughts on this:

cos 57 = sin (90-57) = sin 33

so cos 57 . cosec 33 = cos 57 / sin 33 = sin 33 / sin33 = 1

2 cos 60 = 2 * 1/2 = 1

so the last 2 parts work out to 0

now we have to find cos 70 / sin 20

sin 20 = cos 70 so this comes to 1

so finally the answer is 1

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Answer:

0.7698

Step-by-step explanation:

If you call your random variable $X$ , then what you are looking for is

$P(87 \leq X \leq 123)$

because you want the probability of $X$ being between 87 and 123.

We need a table with of the normal distribution. But we can only find the table with $\mu = 0$ and $\sigma = 1$ . Because of that, first we need to normalize our random variable:

$Z = \frac{X - \mu}{\sigma} = \frac{X - 105}{15}$

(you can always normalize your variable following the same formula!)

now we can do something similar to our limits, to get a better expression:

$\frac{87 - 105}{15} = \frac{-18}{15} = -1.2$

$\frac{123 - 105}{15} = \frac{18}{15} = 1.2$

And we transform our problem to a simpler one:

$P(87 \leq X \leq 123) = P(-1.2 \leq Z \leq 1.2) = P(Z \leq 1.2) - P(Z \leq -1.2)$

(see Figure 1)

From our table we can see that $P(Z \leq 1.2) = 0.8849$ (this is represented in figure 2).

Remember that the whole area below the curve is exactly 1. So we can conclude that $P(Z \geq 1.2) = 0.1151$ (because 0.8849 + 0.1151 = 1). We also know the normal distribution is symmetric, then