[" (1) "7-tan^(-1)x" find "(17)/(dat)" in terms "7y],[(a)-2cos y lim_(y)(b)-2sin cos^(3)y(0)2lim y cos^(2)y=0]

If y = a sin x + b cos x , find (d^2y)/(dx^2) in terms of y.

lim_ (x rarr y) (cos ^ (2) x-cos ^ (2) y) / (x ^ (2) -y ^ (2))

Evaluate: underset(x rarr y)lim (cos^(2)x - cos^(2)y)/(x^(2) - y^(2))

Evaluate : lim_(xrarry)(cos^2x-cos^2y)/(x^2-y^2)

lim_ (y rarr x) (y cos xx cos y) / (yx)

If y= sin (sin x) then y _(2) + (tan x) y _(1) + y (cos ^(2) x)=

If tan x=(1)/(7) and tan y=(1)/(3) show that cos 2x = sin 4y

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)

Solution of differential equation (2x cos y + y ^ (2) cos x) dx (2y sin xx ^ (2) sin y) dx = 0 is (a) x ^ (2) cos y + y ^ (2) sin x = C (b) x cos yy sin x = C (c) x ^ (2) cos ^ (2) y + y ^ (2) sin ^ (2) x = C (d) x cos y + y sin x = C

(dy) / (dx) = - (cos x (3cos y-7sin x-3)) / (sin y (3sin x-7cos y + 7))