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NeX [460]
3 years ago
12

In triangle ABC, AB=c, BC=a, CA=b

Mathematics
1 answer:
quester [9]3 years ago
7 0

Answer:

Step-by-step explanation:

Correct option is

B

AE  

2

=  

9

73

​  

 

C

tanθ=  

8

3

​  

 

Hence

BD=DE=EC=  

3

5

​  

 and △ABC is a right angled triangle.

Now  

cosC=  

2.AC.EC

AC  

2

+EC  

2

−AE  

2

 

​  

 

Or  

AE  

2

=AC  

2

+EC  

2

−2.AC.EC.cosC

Or

=4  

2

+(  

3

5

​  

)  

2

−2.8.  

3

5

​  

.cosC

=16+  

9

25

​  

−  

3

2×4×5

​  

.  

5

4

​  

 

Or

=  

9

169

​  

−  

3

32

​  

 

=  

9

169−96

​  

 

=  

9

73

​  

.

Hence

AE  

2

=  

9

73

​  

.

cosθ=  

2.AE.4

AE  

2

+4  

2

−  

3

5

​  

 

2

 

​  

 

=  

73

​  

 

8

​  

.

Hence

secθ=  

8

73

​  

 

​  

 

Now  

tanθ=  

sec  

2

θ−1

​  

 

=  

64

73

​  

−1

​  

 

=  

8

3

​  

.

solution

Expand-image

Correct option is

B

AE  

2

=  

9

73

​  

 

C

tanθ=  

8

3

​  

 

Hence

BD=DE=EC=  

3

5

​  

 and △ABC is a right angled triangle.

Now  

cosC=  

2.AC.EC

AC  

2

+EC  

2

−AE  

2

 

​  

 

Or  

AE  

2

=AC  

2

+EC  

2

−2.AC.EC.cosC

Or

=4  

2

+(  

3

5

​  

)  

2

−2.8.  

3

5

​  

.cosC

=16+  

9

25

​  

−  

3

2×4×5

​  

.  

5

4

​  

 

Or

=  

9

169

​  

−  

3

32

​  

 

=  

9

169−96

​  

 

=  

9

73

​  

.

Hence

AE  

2

=  

9

73

​  

.

cosθ=  

2.AE.4

AE  

2

+4  

2

−  

3

5

​  

 

2

 

​  

 

=  

73

​  

 

8

​  

.

Hence

secθ=  

8

73

​  

 

​  

 

Now  

tanθ=  

sec  

2

θ−1

​  

 

=  

64

73

​  

−1

​  

 

=  

8

3

​  

 

solution

Expand-image

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=\frac{12x + 11}{x^2 +3x-2x - 6}

=\frac{12x + 11}{x(x +3) -2(x +3)}

\therefore \frac{12x + 11}{x^2 +x - 6}=\frac{12x + 11}{(x +3) (x - 2)}

\therefore \frac{12x + 11}{x^2 +x - 6}=\frac{A}{(x +3)}+\frac{B}{(x - 2)}

\therefore \frac{12x + 11}{x^2 +x - 6}=\frac{A(x-2)+B(x+3)}{(x-2)(x+3)}

\therefore 12x + 11 = A(x-2)+B(x+3)

\therefore 12x + 11 = Ax-2A+Bx+3B

\therefore 12x + 11 = Ax+Bx-2A+3B

\therefore 12x + 11 = (A+B) x-2A+3B

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- 2A + 3B = 11... (2)

Solving equations (1) & (2), we find:

A = 5, B = 7

\therefore \frac{12x + 11}{x^2 +x - 6}=\frac{5}{(x +3)}+\frac{7}{(x - 2)}

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