KARNATAKA-2nd-PUC-2023-Mathematics-Sample-Paper
KARNATAKA 2nd PUC 2023 Mathematics Sample Paper
Question 19
$\int \dfrac{1-sinx}{cos^2x}$ $dx$
Solution
The correct answer is $tanx$ - $secx$ + $C$
Explanation
$\int \dfrac{1-sinx}{cos^2x}$ $dx$
$\int \left( \dfrac{1}{cos^2x} - \dfrac{sinx}{cos^2x} \right)$ $dx$
$\int \dfrac{1}{cos^2x}$ $dx$ - $\int \dfrac{sinx}{cos^2x}$ $dx$
$\int sec^2x$ $dx$ - $\int secx tanx$ $dx$
$tanx$ - $secx$ + $C$
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