6.1 Day 2 Applications of Fundamental Identities

Factor the expression and use the fundamental identities to simplify the result:  $\frac{\sec^2x-1}{\sec x-1}\$  

•  $\sec x-1$  

•  $\sec x+1$  

•  $\sec x$  

•  $\cos x$  

Factor the expression and use the fundamental identities to simplify the result: $\cos^4x-2\cos^2x-1\ \ \ \$  

Perform the multiplication and use the fundamental identities to simplify the result:  $\left(\sin x+\cos x\right)^2$  

•  $1+2\sin x\cos x$  

•  $\sin^2x+\cos^2x$  

• 1

•  $1-2\sin x\cos x$  

Perform the multiplication and use the fundamental identities to simplify the result:  $\left(\cot x+\csc x\right)\left(\cot x-\csc x\right)$  

Perform the multiplication and use the fundamental identities to simplify the result:  $\left(3-3\sin x\right)\left(3+3\sin x\right)$  

•  $6\cos^2x$  

•  $\cos^2x$  

•  $9-6\sin x-9\sin^2x$  

•  $9\cos^2x$  

Perform the addition and use the fundamental identities to simplify the result:  $\frac{1}{1+\cos x}+\frac{1}{1-\cos x}$  

•  $2\csc^2x$  

•  $2\sin^2x$  

•  $1-\cos^2x$  

Perform the subtraction and use the fundamental identities to simplify the result:  $\tan x-\frac{\sec^2x}{\tan x}$  

Rewrite the expression so that it is not in fractional form:  $\frac{\sin^2y}{1-\cos y}$  

•  $1+\sin y$  

•  $1-\sin y$  

•  $1+\cos y$  

•  $1-\cos y$  

Use trigonometric substitution to write the algebraic expression as a trigonometric function of  $\theta$  :   $\sqrt{x^2-9},\ \ \ \ \ x=3\sec\theta$  

•  $\tan\theta$  

•  $3\tan\theta$  

•  $\sec\theta$  

•  $3\sec\theta$  

Use trigonometric substitution to write the algebraic expression as a trigonometric function of  $\theta$  :   $\sqrt{16-4x^2},\ \ \ \ \ x=2\sin\theta$  

•  $4-2\sin\theta$  

•  $4\sin\theta$  

•  $\cos\theta$  

•  $4\cos\theta$