If sin `x=(sqrt(5))/(3) " and " 0 lt x lt .(pi)/(2)` find the values of
`(i) " sin " 2x " ""(ii) cos 2x "" ""(iii) tan 2x "`

If cos x=(-3)/(5) " and " pi lt x lt .(3pi)/(2) find the value of (i) "sin 2x "" ""(ii) cos 2x "" ""(iii) tan 2x "

If sin x =(3)/(5) " and " 0 lt x lt (pi)/(2) find the value of tan (x)/(2)

If " sin " x =- (1)/(2) " and " pi lt x lt .(3pi)/(2) find the value of (i) " sin "2x , (ii) " cos " 2x (iii) " tan " 2x

if cos x= (-sqrt(15))/(4) " and " (pi)/(2) lt x lt pi find the value of sin x .

if cos x= (-sqrt(15))/(4) " and " (pi)/(2) lt x lt pi find the value of sin x .

if cos x= (-sqrt(15))/(4) " and " (pi)/(2) lt x lt pi find the value of sin x .

If sin x=(sqrt(5))/(3) "and " .(pi)/(3) lt x lt pi find the values of (i) " sin " (x)/(2) " " (ii) " cos " (x)/(2) " " (iii) " tan " (x)/(2)

If tan x=(-4)/(3) " and " .(pi)/(2) lt x lt pi find the values of (i) " sin ".(x)/(2) " ""(ii) cos " .(x)/(2) " ""(iii) tan ".(x)/(2)

if cos x=(3)/(5) " and cos " y=(-24)/(25) " where " .(3pi)/(2) lt x lt 2 pi " and " pi lt y lt .(3pi)/(2) find the values of (i) " sin (x+y) "" ""(ii) cos (x-y) "" ""(iii) tan (x+y) "

If sin x=(12)/(13) "and sin " y= (4)/(5) " where " (pi)/(2) lt x lt pi " and " 0 lt y lt .(pi)/(2) find the values of (i) " sin " (x+y) " "(ii) " cos " (x+y) " "(iii) " tan " (x-y)