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Triss [41]
3 years ago
7

Simplify quantity 1 minus cosine squared theta divided by sine squared theta..

Mathematics
1 answer:
Ulleksa [173]3 years ago
4 0
For this case we have the following fraction:
 (1-cos ^ 2 (θ)) / (sin ^ 2 (θ))
 We must take into account the following trigonometric identity:
 cos ^ 2 (θ) + sin ^ 2 (θ) = 1
 Therefore rewriting we have:
 sin ^ 2 (θ) = 1 - cos ^ 2 (θ)
 Substituting in the given fraction we have:
 (1-cos ^ 2 (θ)) / (sin ^ 2 (θ))
 = (sin ^ 2 (θ)) / (sin ^ 2 (θ))
 = 1
 Answer:
 
1
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In the diagram, StartFraction S Q Over O M EndFraction = StartFraction S R Over O N EndFraction = 4.
Viktor [21]

Answer:

MN and QR should be used to prove that the triangles are similar by the SSS similarity theorem ⇒ 2nd answer

Step-by-step explanation:

Let us revise the cases of similarity:

  1. AAA similarity : two triangles are similar if all three angles in the first  triangle equal the corresponding angle in the second triangle
  2. AA similarity : If two angles of one triangle are equal to the corresponding angles of the other triangle, then the two triangles  are similar.  
  3. SSS similarity : If the corresponding sides of the two triangles are  proportional, then the two triangles are similar.  
  4. SAS similarity : In two triangles, if two sets of corresponding sides  are proportional and the included angles are equal then the two  triangles are similar.  

In Δs MNO and QRS

∵ SQ = 60

∵ OM = 15

- Find the ratio between SQ and OM

∴ \frac{SQ}{OM}=\frac{60}{15}=4

∵ SR = 32

∵ ON = 8

- Find the ratio of SR and ON

∴  \frac{SR}{ON}=\frac{32}{8}=4

∵ MN = 12 units

∵ QR = 48

- Find the ratio between QR and MN

∴ \frac{QR}{MN}=\frac{48}{12}=4

- The ratio between the corresponding sides are equal

∴ \frac{SQ}{OM}=\frac{SR}{ON}=\frac{QR}{MN}= 4

- By using the third case of similarity SSS

∴ Δ MNO is similar to Δ QRS by SSS similarity theorem

∴ You should use sides MN and QR

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Okay I got

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Step-by-step explanation:

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