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I am Lyosha [343]
3 years ago
12

Prove that tan22° + tan23° + tan22°. tan23° = 1 ​

Mathematics
2 answers:
postnew [5]3 years ago
7 0

Answer:

Hope you got it....

Step-by-step explanation:

1=tan45∘

1=tan(22∘+23∘)

1=tan22∘+tan23∘1−tan22∘tan23∘

1−tan22∘tan23∘=tan22∘+tan23∘

1=tan22∘+tan23∘+tan22∘tan23∘

It will be the same for any two angles that add up to 45∘.

inn [45]3 years ago
7 0

Answer:

ooo....

Step-by-step explanation:

22° + 23° = 45°

taking tan on both side

or,tan(22° + 23°)=tan45°

or,(tan22° + tan23°)/(1-tan22°. tan23°)=1

or,tan22° + tan23° =1- tan22°. tan23°

or,tan22° + tan23° + tan22°. tan23° = 1 ​

                            proved

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Determine whether the following statement is a tautology, contradiction, or neither (~PVQ) ~Q Tautology Contradiction • Neither
Tom [10]

Answer:

The statement (\lnot P \lor Q)\rightarrow \lnot Q is neither a tautology nor a contradiction.

Step-by-step explanation:

A tautology is a statement that is always true.

A contradiction is a statement that is always false.

We are going to use a truth table to determine whether the statement (\lnot P \lor Q)\rightarrow \lnot Q is a tautology, contradiction, or neither

A truth table shows how the truth or falsity of a compound statement depends on the truth or falsity of the simple statements from which it's constructed.

The statement (\lnot P \lor Q)\rightarrow \lnot Q is compound by these simple statements:

  • \lnot P
  • \lnot Q
  • (\lnot P \lor Q)

and we are going to use these simple statements to build the truth table.

The last column contains true and false values. Therefore, the statement is neither a tautology nor a contradiction.

6 0
3 years ago
C is the circumcenter of triangle PQR. PC = 3x + 7, RC = 5x - 15, & QC = 51 - x
SVETLANKA909090 [29]

Answer:

The value of PC is 40.

Step-by-step explanation:

Consider the complete question is " C is the circumcenter of triangle PQR. PC=3X-7 RC=5X-15 & QC= 51-X What does PC equal?"

All vertices or a triangle are equidistant from its circumcenter.

PC=RC=QC

RC=QC

5x-15=51-x

5x+x=51+15

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x=11

The value of x is 11.

We need to find the value of PC.

PC=3x+7

Substitute x=11 in the above equation.

PC=3(11)+7

PC=33+7

PC=40

Therefore, the value of PC is 40.

7 0
3 years ago
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tatyana61 [14]

Answer:

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The product of three consecutive positive numbers (x - 1), x and (x + 1) is 96 times their sum.
Talja [164]

Step-by-step explanation:

their sum is

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their product is

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96 × 3 = x² - 1

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