1. if csc β = 7/3 and cot β = - 2√10 / 3, Find sec β 2. find cos y and tan y if csc y = -√6 / 2 and cot y > 0.
3. Find tan x and sin x if sec x = 6/5 and sin x > 0.

Step-by-step explanation:

1.

Therefore,

2.

Use the identity

We chose the negative value of the cosine because of the condition where cot y > 0. Otherwise, choosing the positive root will yield a negative cotangent value. Now that we know the sine and cosine of y, we can now solve for the tangent:

3. Recall that sec x = 1/cos x, therefore cos x = 5/6. Solving for sin x,

Solving for tan x:

since proposition states that a number is greater than 25, if is true then the number must actually be greater than 25.

this implies that all possible options, except 24, can be accepted