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Question : 9 of 120
Marks:
+1,
-0
Solution:
‌ Concept: ‌ - Derivatives of Trigonometric Functions: ‌‌sin‌x=cos‌x‌‌cos‌x =−sin‌x‌‌tan‌x=sec2x
‌‌cot‌x=−csc2x‌‌sec‌x =tan‌x‌sec‌‌csc‌x=−cot‌x‌csc - Trigonometric Identities: sin2θ+cos2θ=1 sin‌2‌θ=2‌sin‌θ‌cos‌θ cos‌2‌θ=cos2θ−sin2θ
Calculation:
Let us express
‌ in terms of tan
x ‌ =| 2‌sin‌‌cos‌ |
| (cos2+sin2)+(cos2−sin2) |
=‌| 2‌sin‌‌cos‌ |
| 2cos2‌ |
=‌=tan‌ ∴f(x)=tan−1[‌] =tan−1(tan‌)=‌ And, the first derivative of
f(x)=f′(x)=‌(‌)=‌.
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