Question

Assertion (A) If the anti-derivative of a function $\frac{2-3\sin x}{{\cos }^{2}x}$ is $2\sec x-3\tan x+C$.
Reason (R) $\int {\sec }^{2}xdx=\tan x+C$ and $\int \tan x\sec xdx=\sec x+C$

• A. Both A and R are correct; R is the correct explanation of $A$
• B. Both A and R are correct; $R$ is not the correct explanation of $A$
• C. A is correct; $R$ is incorrect
• D. R is correct; A is incorrect

Answer 1

Answer: (D)

$\int \frac{2-3\sin x}{{\cos }^{2}x}dx$
$\therefore \int \frac{2-3\sin x}{{\cos }^{2}x}dx=\int \frac{2}{{\cos }^{2}x}dx-3\int \frac{\sin x}{{\cos }^{2}x}dx$
$=2\int {\sec }^{2}xdx-3\int \tan x\cdot \sec xdx$
$=2\tan x-3\sec x+C$