Question

19. In triangle ABC, AB = AC = 15 cm and BC = 18 cm. Find : (i) cos B (ii) sin C (iii) tan? B - sec2 B + 2
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Answer 1

Step-by-step explanation:

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Question

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In triangle ABC, AB=AC=15 cm and BC=18 cm. Find:

tan

2

B−sec

2

B+2

Medium

Solution

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Correct option is A)

AB=AC=15, BC=18

Using cosine rule,

AC

2

=BC

2

+AB

2

−2(AB)(BC)cosB

15

2

=18

2

+15

2

−2(15)(18)cosB

cosB=

15

9

cosB=

5

3

cosB=

H

B

=

5

3

Now, using Pythagoras theorem.

H

2

=P

2

+B

2

5

2

=P

2

+3

2

P=4

tan

2

B−sec

2

B+2

= (

B

P

)

2

−(

B

H

)

2

+2

= (

3

4

)

2

−(

3

5

)

2

+2

=

9

16−25+18

= 1