NCERT Class 10 Maths Solutions Chapter - 8 Trigonometry, Ex - 8.4

Ex - 8.4

Question 1.  Express the trigonometric ratios sin A, sec A and tan A in terms of cot A.

Solution

We know that


Question 2.  Write all the other trigonometric ratios of  A in terms of sec A.

Solution

We know that



Question 3.  Evaluate 


Solution




Question 4.  Choose the correct option. Justify your choice.
(i).    9sec2 A - 9tan2 A = 
(A)    1
(B)    9
(C)    8
(D)    0 
(ii).    (1 + tanθ + secθ) (1 + cotθ - cosecθ)
(A)    0
(B)    1
(C)    2
(D)    -1
(iii).    (secA + tanA) (1 - sinA) =
(A)    secA
(B)    sinA
(C)    cosecA
(D)    cosA   
  
(A)    sec2A
(B)    -1
(C)    cot2A
(D)    tan2A

Solution

(i) 9sec2A - 9tan2A 
= 9(sec2A - tan2A)
= 9 (1)            [as sec2 A - tan2 A = 1]
= 9 

Hence alternative (B) is correct.


(ii) (1 + tanθ + secθ) (1 + cotθ - cosecθ) 
 

Hence alternative (C) is correct. 
(iii) (secA + tanA) (1 - sinA) 


(iv)

Question 5.  Prove the following identities, where the angles involved are acute angles for which the expressions are defined.

Solution