Solve: tan(x)-cos^2(x)=sin^2(x)

x = 45 degrees +180 n  where n is an integer

Step-by-step explanation:

tan(x)-cos^2(x)=sin^2(x)

Add cos^2(x) to each side

tan(x)-cos^2(x)+ cos^2(x)=sin^2(x)+ cos^2(x)

tan(x)=sin^2(x)+ cos^2(x)

We know that sin^2(x)+ cos^2(x) = 1

tan (x) =1

Take the inverse tan of each side

tan ^-1 ( tan x) = tan ^-1 (1)

x = 45 degrees +180 n  where n is an integer

< xcy ≅ < xby

step-by-step explanation:

in δcax and δbax,

so, δcax ≅ δbax (side-angle-side or sas)

since δcax ≅ δbax, we can conclude < acx ≅ < abx

in δacy and δaby,

so, δacy ≅ δaby (side-angle-side or sas)

since δacy ≅ δaby, we can conclude < acy ≅ < aby

now,

< acy ≅ < aby

=> < acx + < xcy ≅ < abx + < xby

=> < acx + < xcy ≅ < acx + < xby   (since < acx ≅ < abx already proved above)

subtracting < acx from both sides, we get

< acx + < xcy -< acx ≅ < acx + < xby -< acx

cancelling out < acx and -< acx from both sides, we get

< xcy ≅ < xby (proved)