If sinA+cosecA=3 find the value of sin2A+cosec2A

Step-by-step explanation:

Let , we proceed to transform the expression into an equivalent form of sines and cosines by means of the following trigonometrical identity:

(1)

(2)

Now we perform the operations:

(3)

By the quadratic formula, we find the following solutions:

and

Since sine is a bounded function between -1 and 1, the only solution that is mathematically reasonable is:

By means of inverse trigonometrical function, we get the value associate of the function in sexagesimal degrees:

Then, the values of the cosine associated with that angle is:

Now, we have that , we proceed to transform the expression into an equivalent form with sines and cosines. The following trignometrical identities are used:

(4)

(5)

If we know that and , then the value of the function is:

hello from mrbilldoesmath!

answer:

a(n) - a(n-1) -3

discussion:

this ones a bit interesting. given a(n) = 5 - 3n consider this:

a(n-1) = 5 - 3(n-1)

          = (5 - 3n) + 3             => but a(n) = 5 - 3n, the first term

          = a(n)   + 3                 => subtract 3 from both sides

a(n-1) -3 = a(n)  

or

a(n) - a(n-1) -3

you,

mrb