If 5cos^2θ + 6sin^2θ =11/2
, the value of cosecθ =

Step-by-step explanation:

Please refer to the attachment below.

We have:

Remember that cosine is the ratio of the adjacent side to the hypotenuse. Therefore:

And sine is the ratio of the opposite side to the hypotenuse. Therefore:

Substitute into our original equation:

Square:

Multiply both sides by c squared:

Let’s also multiply both sides by 2 to eliminate the fraction:

Remember that according to the Pythagorean Theorem:

Hence, we can make another substitution:

Distribute:

Subtract 10b² from both sides:

Subtract 11a² from both sides:

Take the square root of both sides:

Hence, a is equivalent to b.

Then, we must have a 45-45-90 Triangle.

Therefore, our angle θ is 45°.

We can substitute this back into our original equation to make sure. Remember that cos(45)=sin(45)=√2/2:

Hence: