NCERT Solutions Class 12

Miscellaneous

Find the value of the following:

1.  

Ans. 

= 

= 

= 

=  i.e., , value of  lies in I quadrant.

=  = 

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2.  

Ans. 

= 

= 

= 

=  i.e., , value of  lies in I quadrant.

=  = 

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3. Prove that:  

Ans. Let   so that 

 

 

Since 

=  =  = 

 

 

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4. Prove that:  

Ans. Let  so that 

 

 

Again, Let  so that 

 

 

Since 

= 

= 

 

 

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5. Prove that:  

Ans. Let  so that 

 

Again, Let  so that 

Since  = 

= 

 

 

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6. Prove that:  

Ans. Let  so that 

Again, Let  so that 

 

Since  = 

= 

 

 

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7. Prove that:  

Ans. Let  so that 

 

Again, Let  so that 

Since  = 

= 

 

 

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8. Prove that:  

Ans. L.H.S. = 

= 

= 

= 

= 

= 

= 

R.H.S.

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9. Prove that:  

Ans. Let  so that 

 

 

= 

= 

= 

= 

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10. Prove that:  

Ans. We know that   = 

Again,  

= 

L.H.S. = 

= 

= 

= 

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11. Prove that:  

Ans. Putting  so that 

L.H.S. = 

= 

= 

= 

Dividing every term by 

= 

= 

=  = 

=  = R.H.S.

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12. Prove that:  

Ans. L.H.S. = 

= 

=  …(i) 

Now, let  so that 

From eq. (i),  = R.H.S.

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13. Solve the equation:  

Ans. 

 

 

 

 

 

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14. Solve the equation:  

Ans. Putting 

 

 

 

 

 

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15.  is equal to:

(A)  

(B)  

(C)  

(D) 

Ans. Let  where  so that 

 

Putting 

 

Therefore, option (D) is correct.

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16.  then  is equal to:

(A) 

(B)  

(C) 0

(D)  

Ans. Putting  so that 

 

 

 

 

 

  

 

 

  or 

  or 

But  does not satisfy the given equation.

Therefore, option (C) is correct.

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17.  is equal to:

(A) 

(B) 

(C) 

(D)  

Ans. 

= 

= 

= 

= 

= 

= 

Therefore, option (C) is correct.