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4.     State whether the following are true or false. Justify your answer.

The value of   increases as  increases.
The value of  increases as  increases.
for all values of  .
is not defined for

(i) False, Let A = B = Then,    (ii) True, Take  whent   = 0 then zero(0),   = 30 then value of  is 1/2 = 0.5  = 45 then value of  is 0.707   (iii) False,   (iv) False, Let  = 0    (v) True,   (not defined)

3.     If  and   find

Given that, So, ..........(i) therefore, .......(ii) By solving the equation (i) and (ii) we get; and

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

We need to prove, Taking LHS; Taking RHS; LHS = RHS Hence proved.

2. Choose the correct option and justify your choice :

Put the value of The correct option is (C)

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

[Hint : Simplify LHS and RHS separately]

We need to prove- Taking LHS; Taking RHS; LHS = RHS Hence proved.

2. Choose the correct option and justify your choice :

is true when =

The correct option is (A) We know that  So,

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

Given equation, ..................(i) Taking LHS; [since ] Hence proved

2. Choose the correct option and justify your choice :

The correct option is (D) We know that  So,

2.  Choose the correct option and justify your choice :

Put the value of tan 30 in the given question- The correct option is (A)

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

We need to prove - Taking LHS; [we know the identity ] Hence proved.

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

We need to prove - Taking LHS; By rationalising the denominator, we get; Hence proved.

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

, using the identity

We need to prove - Dividing the numerator and denominator by , we get; Hence Proved.

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

[Hint : Write the expression in terms of and ]

We need to prove- Taking LHS; By using the identity a3 - b3 =(a - b) (a2 + b2+ab) Hence proved.

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

We need to prove- taking LHS;   = RHS Hence proved.

1.        Evaluate the following :

.....................(i) We know the values of- By substituting all these values in equation(i), we get;

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

We need to prove- Now, taking LHS,                                                                        LHS = RHS Hence proved.

1.     Evaluate the following :

..................(i) It is known that the values of the given trigonometric functions, Put all these values in equation (i), we get;

1.     Evaluate the following :

we know the value of   ,  and , After putting these values

1.     Evaluate the following :

We know the value of   and   According to question,

4.    Choose the correct option. Justify your choice.

The correct option is (D) ..........................eq (i) The above equation can be written as; We know that  therefore,
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