Prove that: `("sin"(x+y))/("sin"(x-y))=(t a n x+t a n y)/(t a n x-t a n y)`

Evaluate the following limit: (lim)_(x->0)(a^(t a n x)-a^(sin x))/(t a n x-sin x),\ a >0

x=a(cos t + log tan t/2), y =a sin t

x=y ln(xy),t h e n

x = a (cos t + sin t), y = a (sin t-cos t)

If x=a(cos t+t sin t) and y=a(sin t-t cos t)

Prove that (i) cos (n + 2) x cos (n+1) x +sin (n+2) x sin (n+1) x = cos x) (ii) " cos " .((pi)/(4)-x) " cos " .((pi)/(4)-y) " - sin " ((pi)/(4)-x ) " sin " ((pi)/(4) -y) =" sin " (x+y)

x=a (t-sin t) , y =a (1-cos t)

If sin2x=n sin 2y , then the value of (tan(x+y))/(tan(x-y)) is :

x=a cos t, y=b sin t

Three traveling sinusoidal waves are on identical strings. with the same tension. The mathematical forms of the waves are y_1(x,t) =y_(m) sin(3x- 6t), y_2(x,t)= y_m sin(4x - 8t), and y_(3) (x,t) sin(6x-12t), where x is in meters and t is in seconds. Match each mathematical form to the appropriate graph below: