What is the value of sin⁡2x given that sin⁡x+cos⁡x+tan⁡x+cot⁡x+sec⁡x+csc⁡x=7?

Answer 1

Seven questions and no work shown, but variations of the same name. Please use the same name for your posts.

Answer 2

tanx+cotx = sec^2x/tanx = 1/(sinx cosx)
secx+cscx = (sinx+cosx)/(sinx cosx)
so, we have

sinx+cosx + 2/sin2x + 2(sinx+cosx)/sin2x

See what you can do with that