Answer:
see explanation
Step-by-step explanation:
Using the trigonometric identities
sin²Θ = 1 - cos²Θ , cos²Θ = 1 - sin²Θ
Consider the left side
(sinΘ + cosΘ)(1 - sinΘcosΘ) ← distribute
= sinΘ(1 - sinΘcosΘ) + cosΘ(1 - sinΘcosΘ)
= sinΘ - sin²ΘcosΘ + cosΘ - sinΘcos²Θ
= sinΘ - (1 - cos²Θ)cosΘ + cosΘ - sinΘ(1 - sin²Θ)
= sinΘ - cosΘ + cos³Θ + cosΘ - sinΘ + sin³Θ ← collect like terms
= sin³Θ + cos³Θ
= right side ⇒ proven
Answer:
The value of AD=1 and DC=3
Step-by-step explanation:
Given: ΔABC, D∈ AC m∠ABC=m∠BDA, AB=2, AC=4
Diagram: Please find attachment.
To find: AD=? and DC=?
Calculation:
In ΔABC and ΔADB
∠ABC=∠ADB (Given)
∠A=∠A (Common)
Therefore, ΔABC ≈ ΔADB by AA similarity
If two triangles are similar then ratio their corresponding sides are equal
Therefore,
where, AD=?, AB=2, AC=4
AD=1
AD+DC=AC
1+DC=4
DC=4-1
DC=3
Hence, The value of AD=1 and DC=3
Answer:
- Seat 1: Peter
- Seat 2: Lia
- Seat 3: Kenny
- Seat 4: Jennie
- Seat 5: Harvey
- Seat 6: Joyce
- Seat 7: Rick
- Seat 8: Mark
Step-by-step explanation:
From Rule 6: Jennie is at Seat 4 and next to Harvey; and by rule 1 (Harvey has a higher seat number than Jennie)
- Seat 4: Jennie
- Seat 5: Harvey
From Rule 2: Peter is across from Harvey.
Since Seat 5 is across from Seat 1
From Rule 7: Peter is next to Lia.
Therefore, Lia can either be in Seat 2 or Seat 8, but by Rule 3 (Neither Joyce nor Lia is in seat 8), therefore, Lia is in Seat 2.
By Rule 5: Lia is next to Kenny, therefore:
From Rule 4: Rick is across from Kenny, and Rick is also next to Joyce.
Seat 7 is across from Seat 3, therefore:
Since Rick is also next to Joyce (and by Rule 3, Joyce cannot be on Seat 8)
Therefore, we have:
Seat 1: Peter
Seat 2: Lia
Seat 3: Kenny
Seat 4: Jennie
Seat 5: Harvey
Seat 6: Joyce
Seat 7: Rick
Since Mark has the remaining seat, Mark is on Seat 8.
Q1
Q2 <em>D</em>
sry I don't hv time to ans more
