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cos x, (1- sin x)(2 - sin x), cos x, , 17., , Sol. Let I= | Gein sina) “O, . dt, Put sin x = ¢. Therefore cos x = We => cos x dx = dt,, . J 1 (2-t)-(1-t), From (i), d_p2-b —pD2-H dt = “d-bp2-b- —p2-H dt, , [. Difference of two factors in the denominator namely, 1-tand2-tis(2-t)-(l-#)=2-t-1+t=1], , (as (1-2) E ont 5-2), = =a a-n@-)) # |" “ce “ee, , MathonGo 60, , , , Class 12 Chapter 7 - Integrals, , 1 1 1 1, I(a-aty) w= Spa Iga, , , , log !1-¢1 log |2-¢1, ~ —1- Coefficient of t ~ -1 £ Ee, =-log|1-¢|+log|2-t|+e, 2-t, =log|2-t|-log|1-tl|+ec = log Toi|*¢, 2-sin x, Putting ¢ = sin x, = log T-sinx|+°, , , , Remark: Alternative solution for J G-d2-) dt is, 1 A B, , * G-pe@-) * 1-2 * 2