Trigonometric Identities

Which of the following is NOT a Pythagorean identity?

• $\tan^2x+1=\sec^2x$

• $\cos2x\ =\ \cos^2x-\sin^2x$

• $\sin^2x\ +\ \cos^2x=1$

• $1+\cot^2x\ =\ \csc^2x$

Tags

CCSS.HSF.TF.C.8

Simplify:  $\cot x\sin x\sec^2x$ 

•  $\cos x$  

•  $\tan x$  

•  $\csc x$  

•  $\sec x$  

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

Simplify:  $\cos x-\cos x\sin^2x$  

•  $\sin^3x$  

•  $\cos^3x$  

•  $\tan x\sec^2x$  

•  $1$  

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.TF.C.9

Which of the following is false?

• $\sin\left(-x\right)=-\sin\left(x\right)$

• $\cos\left(-x\right)=-\cos\left(x\right)$

• $\tan\left(-x\right)=-\tan\left(x\right)$

• $\cot\left(-x\right)=-\cot\left(x\right)$

Tags

CCSS.HSF.TF.A.4

Simplify:  $\frac{\sin^2x}{1+\cos x}-1$ 

•  $\frac{1-\cos x}{\sin x}$  

•  $0$  

•  $-\cos x$  

•  $\csc x-1$  

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

Simplify:  $\cot^2x-\csc^2x+\sin^2x+\cos^2x$  

• 0

• 2

•  $\tan^2x$  

•  $\sec^2x$  

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.TF.C.8

Simplify:  $\left(\cos x-\sin x\right)^2$ 

•  $1$  

•  $\cos2x$  

•  $\cos2x+\sin2x$  

•  $1-\sin2x$  

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

Which of the following is false?

•  $\sin\left(a+b\right)=\sin a\cos b-\cos a\sin b$  

•  $\cos\left(a-b\right)=\cos a\cos b+\sin a\sin b$  

•  $\tan\left(a+b\right)=\frac{\tan a+\tan b}{1-\tan a\tan b}$  

•  $\tan\left(a-b\right)=\frac{\tan a-\tan b}{1+\tan a\tan b}$  

Tags

CCSS.HSF.TF.C.9

Simplify:  $\sin\left(\frac{x}{2}\right)\cos\left(\frac{x}{2}\right)$  

•  $\cos x$  

•  $\frac{\cos x}{2}$  

•  $\sin x$  

•  $\frac{\sin x}{2}$  

Tags

CCSS.HSF.TF.C.8

CCSS.HSF.TF.C.9

Simplify:  $\frac{1}{1-\tan x}-\frac{1}{1+\tan x}$ 

•  $\tan2x$  

•  $\tan^2x$  

•  $-\tan x$  

•  $\tan x+\tan^22x$  

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSA.APR.D.7