NCERT Solutions For Class 10 Math Chapter – 8 Exercise – 8.2

Posted onAuthorDev Bhardwaj

NCERT Solutions For Class 10 MATH Chapter – 8 Exercise – 8.2

 

Q1.  Evaluate the following:

  • Sin 600Cos 300 + Sin 300 Cos 600 
  • 2 tan2450+ cos2 300 – sin2 600
  • Cos 450/(sec 300+ cosec 300)
  • (sin 300+ tan 450 – cosec 600)/(sec 300 + cos 600 + cot 450)
  • (5 cos2600 + 4 sec2 300 – tan 2 450)/(sin2300 + cos2 300 )

Solution:-

 

  • (√3/2 x √3/2) + (1/2 x 1/2)

= 3/4 + 1/4

= 4/4

= 1

 

  • 2(1)2+ (√3/2)2 –  (√3/2)2

= 2

 

  • 1/√2/(2/√3 + 2)

= 1/√2/(2 + 2√3)/√3)

= (3√2 – √6)/8

 

  • (1/2 + 1 – 2/√3)/(2/√3 +1/2+1)

(43-24√3)/11

  • 5(1/2)2+ 4(2/√3)2 – 12  / (1/2)2 + (√3/2)2

= 67/12

 

Q2. Choose the correct option and justify your choice:

  • 2tan300/1+tan2300=
  • Sin 600(b) cos 600  © tan 600 (d) sin 300

 

 

  • 1 – tan2450/1+tan2450=
  • Tan 900(b) 1 © sin 450   (d) = 0

 

  • Sin 2A = 2 sin A is true when A =
  • O0(b) 300  ( c ) 450  (d)  600

 

  • 2tan300/1-tan2300=
  • Cos 600(b) sin 600   © tan 600    (d) sin 300 

 

Solution:-

 

  • A is correct option.
  • D is correct option.
  • A is correct option.
  • C is correct option.

 

Q3. If  tan ( A + B) = √3 and tan (A – B) = 1/√3 Find A and B.

Solution:-

 

Tan (A + B) = √3

Tan ( A + B) = Tan 600

(A + B) = 600  (I)

Tan (A – B) = 1/√3

Tan ( a – b) = tan 300

  • b) = 300(ii)

Adding (I) and (ii) we get,

A + b + a – b = 600 + 300

2A = 900

A = 450

Putting the values of A in equation (I)

450 + B = 600

B = 600 – 450

B = 150

Thus A  = 450 and B = 150

 

Q4. State whether the following are true or false . Justify your answer.

  • Sin ( A + B) = Sin a + sin  b
  • The value of sin θincreases as θ increases
  • The value of cos θincreases as θ
  • Sin θ= Cos θ for all the values of θ.
  • Cot A is not defined for A = 00.

Solution:-

 

  • False
  • True
  • False