" 13."(cos x)^(y)=(sin y)^(x)

If tan(7x^(@))=(sin x^(@)cos y^(@)+cos x^(@)sin y^(@))/(cos x^(@)cos y^(@)-sin x^(@)sin^(@)) where x+y=134^(@) ,then the least positive integral value of x, is-

Draw the graph of following function y = cos ^ (- 1) (cos x) y = sin ^ (- 1) (sin x) y = cos (cos ^ (- 1) x) y = sin (sin ^ (- 1) x)

Show that (i) cos x+cos y=2 cos (x+y)/(2) cos (x-y)/(2) (ii) cos x-cos y=-2 sin (x+y)/(2) sin (x-y)/(2) (iii) sin x+sin y=2 sin (dot(x)+y)/(2) cos (x-y)/(2) (iv) sin x-sin y=2 cos (x+y)/(2) sin (x-y)/(2)

If (cos ^ (4) x) / (cos ^ (2) y) + (sin ^ (4) x) / (sin ^ (2) y) = 1 then prove that (cos ^ (4) y) / (cos ^ (2) x) + (sin ^ (4) y) / (sin ^ (2) x) = 1

If (cos^4x)/(cos^2y)+(sin^4x)/(sin^2y)=1,"show taht", (cos^4y)/(cos^2x)+(sin^4y)/(sin^2x)=1

[x (cos y) / (x) + y (sin y) / (x)] y = [y (sin y) / (x) -x (cos y) / (x)] x ((dy) / (dx))

cos (x + y), sin (x + y), - cos (x + y) sin (xy), cos (xy), sin (xy) sin2x, 0, sin2y] | = sin2 (x + y)

Solve {x cos((y)/(x))+y sin((y)/(x))}ydx={y sin((y)/(x))-x cos((y)/(x))}xdy

cos4x-cos4y = 8 (cos x-cos y) (cos x + cos y) (cos x-sin y) (cos x + sin y)

Prove that |(1,x,y),(0, sin x, sin y),(0, cos x,cos y)|= sin (x-y)