Simplify the expression.
-$$\frac { \cos \theta } { 1 + \sin \theta } + \tan \theta$$
A) 1
B) $$\sec \theta$$
C) $\sin ^ { 2 } \theta$
D) $\cos \theta + \sin \theta$

Question

Quizplus · Accepted Answer

The expression can be simplified using trigonometric identities. First, rewrite $\tan \theta$ as $\frac{\sin \theta}{\cos \theta}$. Then, find a common denominator for the two fractions, which is $\cos \theta (1 + \sin \theta)$. This gives $\frac{\cos^2 \theta + \sin \theta}{\cos \theta (1 + \sin \theta)}$. Using the Pythagorean identity $\cos^2 \theta = 1 - \sin^2 \theta$, the numerator simplifies to $1$, leaving $\frac{1}{\cos \theta}$, which is $\sec \theta$.

Simplify the Expression cos⁡θ1+sin⁡θ+tan⁡θ\frac { \cos \theta } { 1 + \sin \theta } + \tan \theta1+sinθcosθ​+tanθ

Simplify the Expression $\frac { \cos \theta } { 1 + \sin \theta } + \tan \theta$