Question

Pls help if pls do most important 15 number 20 number 26 number 28 number 30 number 17 number 25 number 22 number 24 number if u know all pls do all or only the one i ask if u don't know . pls i need help i have to show these all tomorrow.

HOPE U DO IT PLS​

Answer 1

Explanation:

15.
`(cotx+1)/(cotx-1) = (cotx+cotx.tanx)/(cotx-cotx.tanx) = (cotx(1+tanx))/(cotx(1-tanx)) = (1+tanx)/(1-tanx) \\`

16.
`(1+cos\alpha )/(sin\alpha ) = (sin\alpha )/(1-cos\alpha )`

`=> (1+cos\alpha )(1-cos\alpha ) = sin^(2) \alpha \\=> 1-cos^(2)\alpha =sin^(2) \alpha \\=> sin^(2)\alpha +cos^(2)\alpha =1\\`

=> The clause is correct

17. Do the same (16)

18.
`(sinx)/(1-cosx)+(sinx)/(1+cosx) = (sinx(1+cosx) + sinx(1-cosx))/((1+cosx)(1-cosx)) = (sinx + sinx.cosx + sinx - sinx.cosx)/(1-cos^(2)x) = (2sinx)/(sin^(2)x )= (2)/(sinx) = 2cosecx`

19.

`(sinA)/(1+cosA) + (1+cosA)/(sinA)=(2)/(sinA) \\=> (sinA)/(1+cosA) + (1+cosA)/(sinA) - (2)/(sinA) \\ = 0\\=> (sinA)/(1+cosA) + ((1+cosA)/(sinA) - (2)/(sinA) \\) = 0\\=> (sinA)/(1+cosA) + (1+cosA-2)/(sinA) = 0\\=> (sinA)/(1+cosA) +(cosA-1)/(sinA) = 0\\=> (sin^(2) A+(cosA-1)(1+cosA))/((1+cosA)sinA)=0\\=> (sin^(2) A+cos^(2) A-1)/((1+cosA)sinA)=0\\=> (0)/((1+cosA)sinA) =0\\`

=> The clause is correct

20. Do the same (18)

21. Left =
`(1)/(cosecA+cotA) = (1)/((1)/(sinA)+(cosA)/(sinA) ) = (1)/((1+cosA)/(sinA) )= (sinA)/(1+cosA)`

Right =
`cosecA-cotA = (1)/(sinA)-(cosA)/(sinA)= (1-cosA)/(sinA) \\`

Same with (16) => Left = Right => The clause is correct

22. Do the same (21)

Too long, i'm so lazy :))))