3) #1 4) +4 64. 1) 12 2) +2 If x = sin(2 tan^' (2)) and y=sir 1) x>y 2) x=y then 3) x=0= y 4) x y na a

If x=sin(2tan^(-1)2)and y=sin((1)/(2)tan^(-1).(4)/(3)) , then prove that y^2 = 1 - x

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

"If "e^(sin(x^(2)+y^(3)))=tan""(y^(2))/(4)+sin^(-1)x," then y'(0) can be "

"If "e^(sin(x^(2)+y^(3)))=tan""(y^(2))/(4)+sin^(-1)x," then y'(0) can be "

"If "e^(sin(x^(2)+y^(2)))=tan""(y^(2))/(4)+sin^(-1)x," then y'(0) can be "

" 1.If sin x+sin y=(1)/(4),cos x+cos y=(1)/(3) then tan((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 sin ^ (- 1) x + sin ^ (- 1) y + sin ^ (- 1) z = pi show that, x ^ (4) + y ^ (4) + z ^ (4) + 4x ^ ( 2) y ^ (2) z ^ (2) = 2 (x ^ (2) y ^ (2) + y ^ (2) z ^ (2) + z ^ (2) x ^ (2))

If sin ^ (- 1) x + sin ^ (- 1) y + sin ^ (- 1) z = pi, show that x ^ (4) + y ^ (4) + z ^ (4) + 4x ^ ( 2) y ^ (2) z ^ (2) = 2 (x ^ (2) y ^ (2) + y ^ (2) z ^ (2) + z ^ (2) x ^ (2))

If y=log (1+ sin x), prove that y_(4)+y_(3)y_(1)+y_(2)^(2)=0 .