Question

Evaluate: $\frac{\sin x+\cos x}{{\cos }^{3}x}=$

• A. $1+\tan x+{\tan }^{2}x-{\tan }^{3}x$
• B. $1+\tan x+{\tan }^{2}x+{\tan }^{3}x$
• C. $1-\tan x+{\tan }^{2}x+{\tan }^{3}x$
• D. $(1+\tan x){\sec }^{2}x$

Answer 1

Answer: (B)

$1+\tan x+{\tan }^{2}x+{\tan }^{3}x$

$\to \frac{\sin x+\cos x}{{\cos }^{3}x}\to {\sec }^{2}x\left(\tan x\right)+{\sec }^{2}x$

$\to \tan x(1+{\tan }^{2}x)+(1+{\tan }^{2}x)$

$\to {\tan }^{3}x+{\tan }^{2}x+\tan x+1$