Solve `sin^2x+cos^2y=2sec^2z` for `x , y ,a n dzdot`

Solve y'=sin^(2)(x-y+1)

Let x ,y ,z in R such that x+y+z=6a nd x y+y z+z x=7. Then find the range of values of x ,y ,a n dzdot

Solve 2 sin^(2) x-5 sin x cos x -8 cos^(2) x=-2 .

Suppose that for some angles xa n dy , the equations sin^2x+cos^2y=(3a)/2a n dcos^2x+sin^2y=(a^2)/2 hold simultaneously. the possible value of a is ___________

Solve x+y+z=2 2x+y-z=6 3x+2y+2z=6

If f(x , y) satisfies the equation 1+4x-x^2=sqrt(9sec^2y+4cos e c^2y) then find the value of xa n dtan^2ydot

For x, y, z, t in R, sin^(-1) x + cos^(-1) y + sec^(-1) z ge t^(2) - sqrt(2pi t) + 3pi The value of x + y + z is equal to

Show that sin(x+y)sin(x-y)= sin^2 x -sin^2 y .Hence prove that sin(x+y)sin(x-y)+sin(y+z)sin(y-z) +sin(z+x)sin(z-x)=0