Q&A - Ask Doubts and Get Answers

Sort by :
Clear All
Q

17. is equal to

(A)

(B)

(C)

(D)

Applying formula: . We get,  Hence, the correct answer is C.

16.  then  is equal to

(A)

(B)

(C)    0

(D)

Given the equation:  we can migrate the  term to the R.H.S. then we have; or                                ............................(1) from     Take       or    . So, we conclude that; Therefore we can put the value of  in equation (1)  we get, Putting x= sin y, in the above equation; we have then,   So, we have the solution;     Therefore we have . When we have , we can see that...

15.   is equal to

(A)

(B)

(C)

(D)

Let then we have;    or Hence the correct answer is D.

Solve the following equations:

14.

Given equation is : L.H.S can be written as;   Using the formula So, we have         Hence the value of .

Solve the following equations:

13.

Given equation ; Using the formula: We can write So, we can equate; that implies that . or          or    Hence we have solution .

Prove that

12.

We have to solve the given equation:   Take as common in L.H.S, or     from      Now, assume,   Then, Therefore we have now, So we have L.H.S then That is equal to R.H.S. Hence proved.

Prove that

11.

[Hint: Put ]

By using the Hint we will put ; we get then,    dividing numerator and denominator by , we get,       using the formula     As L.H.S = R.H.S Hence proved

Prove that

10.

Given that By observing we can rationalize the fraction         We get then, Therefore we can write it as;   As L.H.S. = R.H.S. Hence proved.

Prove that

9.

By observing the square root we will first put . Then, we have or, R.H.S. . L.H.S. hence L.H.S. = R.H.S proved.

Prove that

8.

Applying the formlua:     on two parts. we will have,     Hence it s equal to R.H.S Proved.

Prove that

7.

Taking R.H.S; We have Converting sin and cos terms in tan forms: Let    and   now, we have    or                        ............(1) Now,                              ................(2) Now, Using (1) and (2) we get, R.H.S.     as we know so, equal to L.H.S Hence proved.

Prove that

5.

Take   and     and then we have, Then we can write it as:     or                                       ...............(1) Now,    So,                          ...................(2) Also we have similarly;   Then,              ...........................(3) Now, we have L.H.S     so, using (1) and (2) we get,                      or we can write it as;    =  R.H.S. Hence proved.

Prove that

4.

Taking    then, Therefore we have-               .............(1). , Then,                     .............(2). So, we have now, L.H.S. using equations (1) and (2) we get,                            =  R.H.S.

Prove that

3.

To prove: ; Assume that    then we have . or  Therefore we have   Now, We can write L.H.S as        as we know           L.H.S = R.H.S

Find the value of the following:

2.

We have given ; so, as we know  So, here we have . Therefore we can write  as:               .

Find the value of the following:

1.

If   then   , which is principal value of . So, we have       Therefore we have, .

21.   is equal to

(A)

(B)

(C)    0

(D)

We have ; finding the value of  : Assume  then,   and the range of the principal value of  is . Hence, principal value is  Therefore  and  so, we have now, or,  Hence the answer is option  (B).

20.  is equal to

(A)

(B)

(C)

(D)

Solving the inner bracket of ;   or Take   then,   and we know the range of principal value of  Therefore we have . Hence,  Hence the correct answer is D.

19.  is equal to

(A)

(B)

(C)

(D)

As we know that  if  and is principal value range of . In this case , hence we have then,     Hence the correct answer is  (B).

Find the values of each of the expressions in Exercises 16 to 18.

18.

Given that   we can take , then   or                    We have similarly; Therefore we can write              from
Exams
Articles
Questions