5

Q1.

Solution

Q2. Prove that,sin 50^o - sin 70^o + sin 10^o = 0

Solution

Q3. The speed of sound is nearly 341m/s, if a car of wheel radius 70 cm moves with a speed of sound. Find the number of revolutions it will make in 10 sec.

Solution

Let n be the number of revolution a wheel makes in 10 sec.   The distance travelled by the wheel  in 10 sec is 3410 m   Therefore, n x  = 3410    

Q4.

Solution

Q5. Prove that, =

Solution

L.H.S.=            =            =            =

Q6. Prove that, =

Solution

L.H.S. = =+ = = = R.H.S. Hence proved.

Q7.

Solution

Q8.

Solution

Q9. Prove that,

Solution

L.H.S.= = = =   Hence proved.

Q10. Evaluate sin105^o + cos105^o.

Solution

sin105^o + cos105^o = sin (60^o + 45^o) + cos (60^o + 45^o)  = sin60^o cos45^o + cos60^o sin45^o + cos60^o cos45^o - sin60^o sin45^o    

Q11. Prove that,Cos (A + B). cos (A - B) = cos² A - sin² B

Solution

Q12.

Solution

Q13. Prove that,

Solution

Q14. If , show that

Solution

squaring both sides hence proved

Q15. Draw the graph of y =

Solution

To draw the graph, we shall first find the values of x in the interval [0, ]. We know that, Hence the graph of the given function is as follows-  

Q16. Draw the graph of y = tanx

Solution

We know that the value of tanx repeats after an interval of . To draw the graph we shall first find the values of tanx for some convenient values of x in [0, ]         We know that tan90^o is not defined, but as the angle x approaches 90^o from left side the value of tanx increases indefinitely. Similarly as the angle x approaches 90^o from right side, the value of tanx decreases indefinitely. Hence the graph of above function is as follows-

Q17. Solve

Solution

 either  or  either  or  either  or  as both cases together give all multiples of we have  where n is an integer.  

Q18. Solve

Solution

     either  or  either  or   either   or  either       where n, m are integers.

Q19. Prove that, =

Solution

LHS=  =          =            = = =      =RHS

Q20.

Solution

Q21. =

Solution

L.H.S.= +             =              =               =               =  

Q22.   Convert  into radian measure.

Solution

As     Therefore   =   1^o =  radians  =  radian = radian=

Q23.

Solution

Hence the value of 

Q24. Given 2A,2B,2C are angles of a triangle, Prove that

Solution

so = so cross multiplying we get Hence proved.  

Q25. Find the angle between the minute hand and the hour hand of a clock when the time is 5:20.

Solution

In 12 hours hour hand moves by 360 degrees In 1 hr it will move by 30 degrees So in 1 min it will move ½ degree So in 5 hr and 20 min it will move 5 x 30 + 20 x ½ = 160 degree For minute hand In 60 min it moves 360 degree So in 1 min it moves 6 degree. So in 20 min it moves 20x6 =120 degree. Therefore difference is 160 – 120 = 40 degree

Q26. What is the value of

Solution

    (1).(-1)(1)…………..51terms. So in the whole series there are 26 terms which is 1 and 25 terms (-1) So product of 25 (-1)^’s  is (-1) Hence, is -1.

Q27. Prove that, =

Solution

L.H.S. = =  =  = R.H.S. Hence proved.

Q28.

Solution

Q29. Solve

Solution

either  or  either  or   either   or  or  where n, m are integers.

Q30. =

Solution

L.H.S.= = = = = = = = =R.H.S. Hence proved.

Q31. Prove that, =

Solution

L.H.S.= dividing the expression by = = = = = =R.H.S. Hence proved.

Q32. Draw the graph of y = cos2x,

Solution

         So, the graph of above function is as follows-

Q33. If  find the value of

Solution

Using tan(x+y) we have =_, === Substituting the values we get, ==2

Q34. Prove that,

Solution

L.H.S.= = = = = = = = =R.H.S.

Q35. Solve

Solution

 dividing the equation by 2 through out, we get    where n is an integer

Q36.

Solution

Q37.

Solution

Q38. What is the value of the supplementary angle to the sum of .

Solution

Q39.

Solution

Q40. Evaluate:

Solution

 

Q41.

Solution

Q42. Prove that,

Solution

L.H.S.= = =[ using the property  and ] = =R.H.S. H ence proved.

Q43.

Solution

Q44.

Solution

= = = = = = =R.H.S. Hence proved.  

Q45. Prove that,

Solution

L.H.S. =            =            = =   =RHS

Q46.

Solution

Q47.

Solution

Q48.

Solution

Q49. Solve

Solution

 either  or  either  or  either  or  where n,m are integers

Q50.

Solution

Q51. Calculate cos15^o

Solution

cos15^o = cos(45^o – 30^o)              = cos45^ocos30^o + sin45^o sin30^o                          

Q52.

Solution

Q53.  Convert 22.22^c into degree measure.

Solution

We know that    1^c  =    So degree measure =   Radian   Degree measure = =     hence