Trig Identities

Simplify

  $\csc\ x\left(\cos x+\sin x\right)$  

• csc x

• tan x + 1

• cot x

• cot x + 1

Tags

CCSS.HSF.TF.C.9

Simplify

 $\sin\theta\left(\csc\theta-\sin\theta\right)$  

• secθ

• cos²θ

• sin²θ

• sin²θ/cos²θ

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

Simplify
(sec x)(cot x)(sin x)

• sin x
• - sin x
• 1
• -1

Tags

CCSS.HSF.TF.C.8

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

•  $\sin^2x$  

•  $\cos^2x$  

•  $\sin^3x$  

•  $\cos^3x$  

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.TF.C.8

CCSS.HSA.APR.D.7

Simplify:  $\sec x-\tan x\sin x$  

•  $\sin x$  

•  $\cos x$  

•  $\csc x$  

•  $\sec x$  

Tags

CCSS.HSF.TF.C.9

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

 $\cos75^o\cos15^o-\sin75^{o\ }\sin15^o$  is equivalent to

•  $\sin\ 90^{o\ }$  

•  $\sin\ 60^{o\ }$  

•  $\cos\ 90^{o\ }$  

•  $\cos\ 60^{o\ }$  

Tags

CCSS.HSF.TF.C.9

Use sum or difference angles identity to find the exact value for  $\cos105^o$  

•  $\frac{\sqrt{6}+\sqrt{2}}{4}$  

•  $\frac{\sqrt{6}-\sqrt{2}}{4}$  

•  $\frac{-\sqrt{6}-\sqrt{2}}{4}$  

•  $\frac{\sqrt{2}-\sqrt{6}}{4}$  

Tags

CCSS.HSF.TF.C.9

Given  $\sin x=\frac{3}{5}and\ \sin y=\frac{2}{3},$  where  $x\ and\ y$  are both in first quadrant.   $Evaluate\ \sin\left(x+y\right)$  

•  $\frac{3\sqrt{5}+8}{15}$  

•  $\frac{4\sqrt{5}+6}{15}$  

•  $\frac{2\sqrt{5}+12}{15}$  

•  $\frac{4\sqrt{5}+2}{5}$  

Tags

CCSS.HSF.TF.C.9

Write the following expression as the sine, cosine, or tangent of an angle.
cos(175)cos(55)+sin(175)sin(55)

• sin(120)
• cos(120)
• cos(230)
• sin(230)

Tags

CCSS.HSF.TF.C.9

Use a double-angle or half-angle identity to find the exact value of each expression

cos θ = 4/5 and 270° < θ < 360°Find sin 2θ

• -1/5

• 24/25

• -24/25

• -25/24

Tags

CCSS.HSF.TF.C.9