(a) Differentiate \sec ^{-1} ( {1}/{\sqrt{1-x^2}}) w.r.t. \sin ^{-1} (2 x \sqrt{1-x^2}). OR (b) If {\y}=\tan x+ \sec x, then prove that { {\d}^2 {\y}}/{ {\d} x^2}=\frac{\cos x}{(1- \sin x)^2}.

CBSE Class 12 Math 2023 Delhi Set 1 Solved Paper - Question 27

Question : 27 of 38

Marks: +1, -0

(a) Differentiate

\ sec ^{-1} (\;{1}/{{√{1-x^2}}})

w.r.t.

sin \;^{-1} (2 x {√{1-x^2}})

.
OR
(b) If

{\y}=\tan x+\ sec x

, then prove that

\;{ {\d}^2 {\y}}/{ {\d} x^2}=\;{\cos x}/{(1- sin \;x)^2}

Solution:

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