Solve this trig identity. (secx - sinx)/cotx = cosx Thanks!?

(secx - sinx) / cotx = cosx

(1/cos(x) - sin(x)) / (cos(x) / sin(x)) = cosx

1/cos(x) - sin(x) = cos(x)(cos(x) / sin(x))

Multiply both sides by sin(x)

sin(x)/cos(x) - sin(x)sin(x) = cos(x)cos(x)

tan(x) - sin²(x) = cos²(x)

tan(x) = cos²(x) + sin²(x)

Remember from your Pythagorean trig identity that: cos²(x) + sin²(x) = 1

Thus

tan(x) = 1

x = π/4, 3π/4, 9π/4, etc.

Tip:

Convert all sec(x), cot(x), etc into sin and cos forms.

sec(x) = 1 / cos(x)

cot(x) = cos(x)/sin(x)

csc(x) = 1 / sin(x)

cosx(secx+cosxcsc^2x)---->remember that secx is only a million/cosx and cscx is only a million/csc^2x cosx (a million/cosx+cosx/sin^2x)-------->now distribute the cosx cosx/cosx+cos^2x/sin^2x----->cosx/cosx is only a million a million+(cos^2x/sin^2x)-------->now a million is likewise an identical as sin^2x/sin^2x ---->you are able to also comprehend that cos^2x/sin^2x=cot^2x and a million+cot^2x=csc^2x sin^2x/sin^2x+cos^2x/sin^2x------>you are able to now combine the numerators because now you've person-friendly denominators (sin^2x+cos^2x)/sin^2x----------->now remember that sin^2x+cos^2x is only a million a million/sin^2x---------->by using definition a million/sin^2x=csc^2x csc^2x