Answer:
The most straightforward way to obtain the expression for cos(2x) is by using the "cosine of the sum" formula: cos(x + y) = cosx*cosy - sinx*siny. cos(2x) = cos² (x) - (1 - cos²(x)) = 2cos²(x) - 1. = 2cos²(x) - 1.
Step-by-step explanation:
Answer:
See explanation
Step-by-step explanation:
<u>Step 1.</u> Substitute for d to solve for n:
From the first equation:

Then substitute it into the second equation:

<u>Step 2:</u> Substitute for n to solve for d:

There are 40 dimes and 30 nikels in the piggy bank
Answer:
The Solution Set
Step-by-step explanation:
Despite missing some context, the output we could get as result of an expression/equation it is what we call a Solution set. A set which makes the initial statement of equation/expression true, therefore valid.

Therefore, the elements of the Solution set, 3 and 4 when plugged into the equation make the statement of the quadratic equation true.

By definitions of the (co)tangent and cosecant function,

Turn everything into fractions with common denominators:

Recall that
, so we can simplify both sides a bit.
On the left:

On the right:

(as long as
, which happens in the interval
when
or
)
So we have




