( \operatorname { sin } \frac { x } { 2 } + \operatorname { cos } \fra

1.	( \operatorname { sin } \frac { x } { 2 } + \operatorname { cos } \frac { x } { 2 } ) ^ { 2 } , x = \frac { \pi } { 6 } \vec { c }
Answer» y = (sin x/2 + cos x/2)^2 => y = sin^2 x/2 + cos^2 x/2 + 2.sin x/2 .cos x/2 => y = 1 + sinx Now differentiate wrt x we get, dy/dx = 0 +cosx = cos x Now, [dy/dx] at x = pi/6 = cos (pi/6) = (root3)/2

( \operatorname { sin } \frac { x } { 2 } + \operatorname { cos } \frac { x } { 2 } ) ^ { 2 } , x = \frac { \pi } { 6 } \vec { c }

Answer»

y = (sin x/2 + cos x/2)^2

=> y = sin^2 x/2 + cos^2 x/2 + 2.sin x/2 .cos x/2

=> y = 1 + sinx

Now differentiate wrt x we get,

dy/dx = 0 +cosx = cos x

Now, [dy/dx] at x = pi/6

= cos (pi/6)

= (root3)/2