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: