#17 Pythagorean Identities

csc(x)sin(x) + cot²(x)

• A. tan²(x)

• B. sec²(x)

• C. csc²(x)

• D. -csc²(x)

On which line is there a mistake when verifying, working the left side?

1)   $\left(\csc x-\cot x\right)^2=\frac{1-\cos x}{1+\cos x}$  

2)   $\left(\frac{1}{\sin x}-\frac{\cos x}{\sin x}\right)^2$  
3)    $\left(\frac{1-\cos x}{\sin x}\right)^2$  
4)    $\frac{\left(1-\cos x\right)^2}{1-\cos^2x}$  
5)    $\frac{\left(1-\cos x\right)\left(1-\cos x\right)}{\left(1-\cos x\right)\left(1+\cos x\right)}$  
6)    $\frac{1-\cos x}{1+\cos x}=\frac{1-\cos x}{1+\cos x}$  

• 3

• 4

• 5

• None. This verified correctly

tan(x)cot(x) + tan²(x)

• A. -sec(x)

• B. cos²(x)

• C. sec²(x)

• D. -sec²(x)

 $\cos^4\theta-\sin^4\theta=$  

•  $\cos\theta-\sin\theta$  
  

•  $1$  
  

•  $-1$  
  

•  $\cos^2\theta-\sin^2\theta$  
  

(1 + cot²u)(1 - cos²u)

sin²x(csc²x - 1)

• A. -cos²(x)

• B. -2

• C. -sin(x)

• D. cos²(x)

(cos(w))(1 + tan²(w))

• A. sin²(w)

• B. -sec(w)

• C. csc(w)

• D. sec(w)

Tags

CCSS.HSF.TF.C.8

(6cscA - 6cotA)(cscA + cotA)

 $\frac{\cos x}{1+\sin x}+\tan x=$  

• csc(x)

• sec(x)

• tan(x)

• cot(x)

(csc²θ)(cos²θ - 1)