Q. Prove that: sec2A+tan2A=tan(45+A)

L.H.S.
= 1 / cos(2a) + sin(2a) / cos(2a)
= (1 + sin(2a)) / (cos(2a))
= (sin^2(a) + cos^2(a) + 2 * sin(a) * cos(a)) / (cos^2(a) - sin^2(a))
= (sin(a) + cos(a))^2 / ((cos(a) - sin(a)) * (cos(a) + sin(a)))
= (cos(a) + sin(a)) / (cos(a) - sin(a))
= cos(a) * (1 + sin(a) / cos(a)) / (cos(a) * (1 - sin(a)/cos(a)))
= (1 + tan(a)) / (1 - tan(a))
= (tan(45) + tan(a)) / (1 - tan(a) * tan(45))
= tan(a + 45)

Read more

Q. Prove that: (2cos2A-1)(2cos2A+1)(2cos4A-1)(2cos8-1)=2cos16A+1

Read more

Q. Prove that: 4(cos^4A+sin^4A)/(cos^4A-sin^4A)=(3+cos4A)Sec2A

Read more

9. Write a program to count the number of words in a sentence.

CLS
INPUT "ENTER ANY STRING"; S$
WC = 1
FOR I = 1 TO LEN(S$)
B$ = MID$(S$, I, 1)
IF B$ = " " THEN
WC = WC + 1
END IF
NEXT I
PRINT "TOTAL NO. OF WORDS= "; WC
END

Read more

11. Write a progra to find whether the supplied word is palindrome or not. A word is called palindrome, if it reads the same from both the sides. (e.g. MADAM)

CLS
 INPUT "Enter a word:"; w$
 FOR i = LEN(w$) TO 1 STEP -1
     m$ = MID$(w$, i, 1)
     rev$ = rev$ + m$
 NEXT i
 PRINT
 PRINT "The original word is "; w$
 PRINT "The reverse wod is "; rev$
 PRINT
 IF w$ = rev$ THEN
     PRINT "The given word is palindrome"
 ELSE
     PRINT "The given word is not palindrome"
 END IF
 END

Read more

Gita can do a piece of work in 3 days which can done by sita in 4 days .if sita can do a piece of work in 5 days which can done by rita in 6 days ,,in how many dayd will gita can do a work can be done by rita 16days?

Read more

Prove that: (sec^2A+1)(sec^4A+1)(sec^8A+1)=tan8A.cotA

Soln:

Read more

Are you appearing in S.E.E. exams? Don't forget to follow the following tips:

"Hard work always does not give you best result, sometimes if you ignore simple work you may even get worst result." So, follow the tips during examination days:-

i. First check materials you need for the exam. e.g. If its maths, calculator. (pens, pencils, instrument box etc)

ii. You should have back up of every materials. e.g. at least two pens of having same ink color.If you use other kind of dot pens then their refills etc.

iii. The very first write down your Symbol Number and just before submission of your answer sheet, recheck it once again; the thing you should not forget is: it should be in neat and clean handwriting.

iv. First you answer or solve the question you know or confident at, after you finish them try to remember and answer those question that you do not know. If you really don't know answer don't panic just take a long breathe and try once; no matter what you write; write related stuff according to the questions. Don't just leave blanks in while answering.

v. Last but not least never disturb other and be disturbed yourself during examination. The 3 hours exam is not going to change your whole life.

Thank You.

"All The Best" - S.E.E. student - 2074

Read more

The sum of the digits of two-digits number is 10. If 18 is added to the number , its digits are reversed. Find the number.

Soln:
Let the two digits number = 10x +y where
tens place digit = x
units place digit = y
according to the first condition
x+y = 10................(1)
according to the second condition
10x + y + 18 = 10y + x
or, 10x- x + y -10y = -18
or, 9x - 9y = -18
x - y = -2..............(2)
solve the equestion 1 & 2 we get
x + y = 10
x - y = -2
´´´´´´´´´´´´´´´´´´´´´´´´
2x = 8
or, x = 4
put the value of x in equation (1) we get
4 + y = 10
or, y = 10 - 4
or, y = 6
so the two-digites number = 10x + y
= 10 × 4 + 6
= 46 Ans.

Read more

The sum of present ages of a brother and his younger sister is 16 years . If the product of their ages is 63. Find their ages.

soln: 
Let the present age of brother = x
and the present age of sister = y
according to the first condition
x + y = 16
or x = 16 - y .......(i)
according to the second condition
xy = 63.........(ii)
solving the equation (i) & (ii), we have,
(16 - y)y = 63
or, 16y - y^2 = 63
or, y^2 - 16y+63 = O
or, y^2 -9y - 6y + 63 = o
or, (y-9)(Y-7) = 0
or, (y - 9) = o
or, y = 9
put the value y in equation (i), we get
x =16 - 9
= 7
so, present age of brother = x = 7 years
and the present age of sister = y = 9 years

Read more