Using Identities to Simplify Trigonometric Expressions

When simplifying trig expressions, which of the following strategies could be helpful (check all that apply):

• Convert everything to sine and cosine

• Draw a picture

• Get a common denominator

• Factor

• Give up

 $\sec\ x=$  

•  $\frac{1}{\sin\ x}$  

•  $\frac{1}{\cos\ x}$  

•  $\frac{1}{\tan\ x}$  

•  $\frac{1}{\csc\ x}$  

Tags

CCSS.HSF.TF.A.2

 $\cot\ x=$  

•  $\frac{\sin x}{\cos x}$  

•  $\frac{\cos x}{\sin x}$  

•  $\frac{\sec x}{\csc x}$  

•  $\frac{\csc x}{\sec x}$  

Tags

CCSS.HSF.TF.A.4

 $\sin^2x+\cos^2x=$  

•  $1$  

•  $-1$  

•  $\tan^2x$  

•  $\cot^2x$  

Tags

CCSS.HSF.TF.A.4

CCSS.HSF.TF.C.8

CCSS.HSF.TF.A.3

 $\sec^2x-\tan^2x=$  

•  $\cot^2x$  

•  $\csc^2x$  

•  $1$  

•  $-1$  

 $\cot^2x-\csc^2x=$  

•  $\sec^2x$  

•  $\tan^2x$  

•  $1$  

•  $-1$  

Simplify  $\sin x\sec x$  

•  $\csc x$  

•  $\tan x$  

•  $\cot x$  

•  $\cos x$  

Simplify  $\cos^2x\left(\sec^2x-1\right)$  

•  $\sin^2x$  

•  $\cos^2x$  

•  $\tan^2x$  

•  $\csc^2x$  

Tags

CCSS.HSF.TF.C.8

CCSS.HSA.SSE.B.3

Simplify  $\tan x-\frac{\sec^2x}{\tan x}$  

•  $\tan x$  

•  $-\tan x$  

•  $\cot x$  

•  $-\cot x$  

Simplify  $\frac{\cos x}{1+\sin x}+\frac{1+\sin x}{\cos x}$  

•  $\frac{2+2\sin x}{\cos x\left(1+\sin x\right)}$  

•  $2\cos x$  

•  $2\sin x$  

•  $2\sec x$