Karan needs to choose between two gym plans. he can either pay a $150 joining fee and a $10 monthly fee, or he can pay a $50 joining fee and a $30 monthly fee. on what month will the cumulative costs of the plans be equal, and what will those total costs be karan will pay a cumulative cost dollars with either plan to go to the gym for months.

Let  x be the month on which the fee for two plans are equal.

Therefore,

150 + 10x = 50 + 30x

10x - 30x = 50 - 150

-20x = -100

x = 5

Cumulative cost = 150 + 10(5)

                           = 150 + 50

                           = 200

Hence, Karan will pay a cumulative cost of $200 dollars with either plan to go to the gym for 5 months.

Hi!

Let's first expand the cotangent of theta.

You'll probably know that tangent will be "y/x", or , and cotangent is the reciprocal of this, meaning that it is "x/y" or .

That means that we are now given this equation.

That'll multiply to:

We'll want a common denominator to add by multiplying to both top and bottom of the second term:

Pythagorean Identity states that , so substitute that in:

Which simplifies to:

Hope this helps!