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Prove the following identity: (1+cos⁡(x)+cos⁡(2x))/(sin⁡(x)+sin⁡(2x) )=cot⁡(x)

Straight away we notice that two trigonometric terms on the left hand side have 2x but there are no 2x on the right hand side therefore we realise that this question will require double angle formulae. If yo...
JB
Answered by Jessica B. • Maths tutor
20146 Views

Given 1/2 + 1 + 2 + 2^2 + ... + 2^10 = a*2^b + c, find the values of a,b,c.

Consider the Left-Hand-Side (LHS) of the equation first. LHS: 1/2 + 1 + 2 + 2^2 + ... + 2^10. We identify this as a geometric series by noticing that dividing any term u_(n+1) by the preceding term n the res...
CM
Answered by Carlo M. • Maths tutor
4383 Views

How can the central bank affect economic activity using monetary policy

A particular economy can go through many downturns and upturns in what is called the business cycle. A central bank may wish to dampen these fluctuations by using one of two tools. The first one is changing ...
MS
Answered by Martin S. • Economics tutor
3682 Views

What is the difference between osmolarity and osmolality?

First of all, it is important to define osmosis. If you have two solutions separated only by a semi-permeable membrane, and one solution is more concentrated than the other, then water will move from the les...
KW
Answered by Kelly W. • Biology tutor
17794 Views

What is the difference between the imperfetto and the passato prossimo?

The translation of the imperfect tense would be "I used to do/ I was doing". Hence, this tense would be used to describe an action in the past that had an unspecified starting or finishing time, it...
HM
Answered by Helena M. • Italian tutor
3225 Views