untitled

or, sec^2 Atan^2 A 1
or, (secAtanA)(secAtanA) 1

or, ( c n ) 1
2

5

seAtaA [from (i)]

∴

5

2

secAtanA

Exercise 9⋅ 1

1. Verify whether each of the following math ematical statements is true or false.
   Give argument in favour of your answer.
   (a) The value of tanA is always less than 1.
   (b) cotA is the multiplication of cot and A.

(c) For any value of A,
5

12

secA.

(d) cos is the smallest form of cotangent.

2. If
   4

3

sinA , find the other trigonometric ratios of the angle A.

3. Given that 15 cotA 8 , find the values of sinA and secA.


4. If ‘C is the right angle of the right angled triangle ABC, AB = 13 cm and BC
   = 12 cm. and ‘ABC θ, find the values of sinθ,cosθ and tanθ.


5. ‘B is the right angle of the right angled triangle ABC. If tanA 3 , verify the

truth of 3 sinAcosA 4.
Prove (6 – 20) :

6. (i) 1 ;
   cosecA

1

secA

1

2  2 (ii) cotA^1 ;

1

cosA

1

2  2 (iii) tanA^1 ;

1

sinA

1

2  2

7. (i) 1 ;
   secA

cosA

cosecA

sinA

 (ii) 1.

cotA

tanA

cosA

secA

 (iii) 1

1 cosec

1

1 sin

1

^2 A ^2 A^

8. (i) c s 1
   1 tn

t

1 cot

tn

˜ 







seAcoecA

aA

coA

A

aA

; (ii) 1

1 cot

1

1 tan

1

^2 A ^2 A^

9. si A A.
   A

A

aA

A

n cos

1 cot

sin

1 tn

cos









10. 
    

    tanA 1 `sin^2 A sinA.

    
    


11. 
    

    secA tanA

    
    

cosecA cotA

cosecA cotA

secA tanA









12. 2 secA.
    cosecA 1

cosecA

cosecA 1

cosecA 2







13. 2 secA.
    1 sinA

1

1 sinA

(^12)




14. 2 tanA.
    cosecA 1

1

cosecA 1

(^12)




15. 2 cosecA.
    sinA

1 cosA

1 cosA

sinA







16. tanA

secA 1

secA 1

tanA