Plzz ans the 1st question in all step explntion

Plzz ans the 1st question in all step explntion EXAMPLE 90 Let 1 Ans. (d) y = ( 3 COS d2y + x g_y_ dx2 dx [JEE (Main) 201. SOLUr10N We have, y = cos ( 3 cos¯ 1 x) This exercise contains multiple choice questions. Each question then gy- is 1. If y = ccs¯ 2 -2 (a) for all x 2 1 2. lfx=fYo (a) 2y (b) 4y -2 for all IÅ>I (b) 2 (d) none of these dx2 (c) 8y

Dear Student,
Put x=tanθi.e cos-12tanθ1+tan2θ cos-1sin2θ        since2tanθ1+tan2θ=sin2θ=cos-1cosπ2-2θ=π2-2θ=π2-2tan-1xNow differentiating it w.r.t. 'x'=-21+x2since x=tanθ       Range of tanθ is from  -,Therefore x can have any value.Hence option A is correct.
Regards.

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