Question

PLEASEE HELPPMEEE!!!!

cot2x+sec2x=tan2x+csc2x

and

1+2sinxcosx/sinx+cosx=sinx + cosx

Answer 1

let 2x = y, then
coty + secy = tany + cscy

cosy/siny + 1/cosy = siny/cosy + 1/siny
(cos^2 y + siny)/ sinycosy = sin^2 y + cosy)/sinycosy
cos^2 y + siny = sin^2 y + cosy
cos^2 y - sin^2 y = cosy - siny
(cosy + sinY )(cosy-siny) = cosy - siny
cosy + siny = 1
square both sides
cos^2 y + 2sinycosy + cos^2 y = 1
2sinycosy = 0
sin2y = 0

2y = 0, 180° , 360° , ....
y = 0, 90°, 180°, ...
but period of sin2y is 180°
so other answers are
90+180 = 270

so y = 0, 90, 180, 270, 360, ...
but y = 2x
so x = 0, 45, 90, 135, 180, ...

however, tangent is undefined for 90
cotangent is undefined for 0
csc is undefined for 0, 180, 360
sec is undefined for 90, 270 ...

so there is no solution.
Check your typing.


for the second, I am not sure of your typing,
if you meant it the way you typed it, then .....

1+2sinxcosx/sinx+cosx=sinx + cosx
1 + 2cosx + cosx = sinx + cosx
2cosx = -1
cosx = -1/2
x = 120° or x = 240°

If you meant
(1+2sinxcosx)/(sinx+cosx)=sinx + cosx
(sin^2 x + cos^2 x + 2sinxcosx) /(sinx+cosx) = sinx+cosx
(sinx + cosx)^2/(sinx+cosx) = sinx + cosx
sinx + cosx = sinx + cosx

Ls = RS
this is an identity.