`cosx+secx=2=>cos^m x+sec^m x=1-1 1`

If cosx+secx=2," then "cos^nx+sec^nx is equal to

Let f(x)= |{:(secx,cosx, sec^2x+cotx cosecx), (cos^2x, cos^2x, cosec^2x),(1,cos^2x, cos^2x):}| Prove that int_0^(pi//2)f(x)dx=-pi/4-8/(15) .

If sin x+cos x=m and sec x+cos ecx=n prove that n(m^(2)-1)=2m

Differentiate : (i) ((sinx + cosx)/(sinx - cos x)) , (ii) ((sec x - 1)/(secx + 1))

If m=sinx+cos x+tan x+cot x+sec x+cosec x and n=sinx+cosx-tanx-cotx-secx-cosecx then (m+n-2)(m-n)=( where x is an acute angle )

If sinx+cosx=m and secx+cosecx=n prove that n(m^2-1)=2m

Let f(x)=|[secx,cosx,sec^2x+cotxcos ecx],[cos^2x,cos^2x, cosec^2x],[1,cos^2x,cos^2x]| then, int_-pi^(pi)f(x)dx equals

Let f(x)=|[secx,cosx,sec^2x+cotxcos ecx],[cos^2x,cos^2x, cosec^2x],[1,cos^2x,cos^2x]| then, int_-pi^(pi)f(x)dx equals

lim _(xto0) ((cos x -secx )/(x ^(2) (x+1)))=