Hardayal Public School Holiday Assignment of ... - Educomp Online

⎛ ⎞k. tan -1 ⎜ x ⎟−1⎛ 1⎟ ⎞+ Sec ⎜⎜2 ⎟2⎝ 1 − x ⎠ ⎝ 1 − x ⎠dy37. Find in each case :dxl. Sin ( )-1 22 x 1 − x(i)22 at b (1 − t )x = , y =221 + t 1 + t(ii) x = 3Cos φ – Cos 3 φ, y = 3 Sin φ – Sin 3 φ(iii) x = a(Cos φ + φ Sin φ) y = a(Sin φ – Cos φ)(iv) x = e t (Cos t + Sin t), y = e t (Cos t – Sin t)(v) xy log (x + y) = 1 (vi) 2 x + 2 y = 2 x + y(vii) x 3 + y 3 = Sin(x + y) (viii) log2 2−1⎛ y ⎞x + y = tan ⎜ ⎟⎝ x ⎠(ix) Sin ( xy ) +x 2= x −yy (x) tan (x + y) + tan (x – y) = 1(xi) Log Sin x + Cos (xy) + e xy = 0 (xii) y x = x y(xiii) y x + x y + x x + y y = a b (xiv) y =Sin xCos x(xv) ( Cot x ) + x ) = y(xvii)(xix)Sin x Sin 2 x.Sin 3 xxxx2xCos x x − 1(tan (xvi) x + = y2x + 1x. (xviii) ( x ) = y2334( 2 x − 1) .( x − 5)yxy =.( xx )( Cos x ) = ( Cos y )112 23( x − 1) (3 x + 1)38. (i) Differentiate log (1 + x 2 ) w.r. to tan -1 x(ii)− ⎛ Cos x⎟ ⎞tan 1 ⎜ w.r. to Sec -1 x⎝ 1 + Sin x ⎠(iii)2Cos −1⎛ 1 − x⎟ ⎞⎜2⎝ 1 + xw.r. to −1⎛ 2 x⎠⎟ ⎞tan⎜2⎝ 1 − x ⎠−12(iv) Sin ( 4 x 1 − 4 x )− 13(v) Sin ( 3 x − 4 x )(vi)tan1 + tan− 1W.r.tw.r. toxw.r. to tan − 1−1xtanx1 − 4 x−1⎛⎜⎜⎝2x1 − x2⎞⎟⎟⎠xdy39. Find if : dx