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:

the entire expression should be subtracted from 30. to subtract the quantity, distribute the negative sign, which changes the signs on the terms. so, the –2 changes to positive and gets added to 30 instead of subtracted from it.

hope this ! ^w^

step-by-step explanation:

i believe its "c" because all of the other options include a but it could be d because there is a way of financing with cash at certain places but its uncommon.