Problem

16. An equivalent expression to $\frac{\sin x+\cos x}{\csc x+\sec x}$ is

Answer

Expert–verified
Hide Steps
Answer

\(\boxed{\frac{\sin(2x)}{2}}\)

Steps

Step 1 ：An equivalent expression to $\frac{\sin x+\cos x}{\csc x+\sec x}$ is

Step 2 ：Convert the expression into sine and cosine terms: $\frac{\sin x+\cos x}{\frac{1}{\sin x}+\frac{1}{\cos x}}$

Step 3 ：Find a common denominator for the denominator: $\frac{\sin x+\cos x}{\frac{\sin x + \cos x}{\sin x \cos x}}$

Step 4 ：Simplify the expression: $\frac{\sin x \cos x(\sin x+\cos x)}{\sin x + \cos x}$

Step 5 ：Cancel out the common terms: $\sin x \cos x$

Step 6 ：Use the double angle identity: $\frac{\sin(2x)}{2}$

Step 7 ：\(\boxed{\frac{\sin(2x)}{2}}\)

link_gpt

Popular Problems

Compute $\int_{0}^{\ln (2) / … Solve the triangle. \[ \mathr… QUESTION 2 - 1 POINT Solve th… 5. Suppose you are a computer… Answer the statistical measur… $(-\infty, 2) \cap(-6, \infty… A firm does not pay a dividen… Math 112 Section: 4. Tubercul… Find $y^{\prime}$ if $y=\ln \… 3. (3pts) Cherry trees in a c… More