NCERT solutions for class 10 Maths
Chapter 8
Coordinate Geometry
Exercise 8.2
Ex 8.2 Question 1.
Evaluate the following:
(i) sin 60° cos 30° + sin 30° cos 60°
(ii) 2 tan2 45° + cos2 30° – sin2 60
Solution :
(i) sin 60° cos 30° + sin 30° cos 60°
sin 30° = 1/2
cos 30° = √3/2
sin 60° = √3/2
cos 60°= 1/2
putting the values of
sin 60° cos 30° + sin 30° cos 60°
= √3/2 ×√3/2 + (½) ×(½ ) = 3/4+1/4
= 4/4
=1
(ii) 2 tan2 45° + cos2 30° – sin2 60
sin 60° = √3/2
cos 30° = √3/2
tan 45° = 1
putting the values of
2 tan2 45° + cos2 30° – sin2 60
= 2(1)2 + (√3/2)2-(√3/2)2
= 2 + 3/4 – 3/4
= 2
(iii) cos 45°/(sec 30°+cosec 30°)
cos 45° = 1/√2
sec 30° = 2/√3
cosec 30° = 2
putting the values of
multiply numerator and denominator by √2,
sin 30° = 1/2
tan 45° = 1
cosec 60° = 2/√3
sec 30° = 2/√3
cos 60° = 1/2
cot 45° = 1
putting the values of
cos 60° = 1/2
sec 30° = 2/√3
tan 45° = 1
sin 30° = 1/2
cos 30° = √3/2
(5cos260° + 4sec230° – tan245°)/(sin2 30° + cos2 30°)
= 5(½)2+4(2/√3)2-12/(½)2+(√3/2)2
= (5/4+16/3-1)/(¼+¾)
= (15+64-12)/12/(4/4)
= 67/12
Ex 8.2 Question 2.
Choose the correct option and justify your choice :
(i) 2tan 30°/1+tan230° =
(A) sin 60° (B) cos 60° (C) tan 60° (D) sin 30°
(ii) 1-tan245°/1+tan245° =
(A) tan 90° (B) 1 (C) sin 45° (D) 0
(iii) sin 2A = 2 sin A is true when A =
(A) 0° (B) 30° (C) 45° (D) 60°
(iv) 2tan30°/1-tan230° =
(A) cos 60° (B) sin 60° (C) tan 60° (D) sin 30°
Solution :
(i) Putting the value of tan 30°
tan 30° = 1/√3
2tan 30°/1+tan230° = 2(1/√3)/1+(1/√3)2
= (2/√3)/(1+1/3) = (2/√3)/(4/3)
= 6/4√3 = √3/2 = Sin 60°
Hence , Correct answer is (A).
(ii) Putting the value of tan 45°
tan 45° = 1
1-tan245°/1+tan245° = (1-12)/(1+12)
= 0/2 = 0
Hence , Correct answer is (D).
(iii) Sin 0° = 0
Hence , Correct answer is (A).
(iv) Putting the value of tan 30°
tan 30° = 1/√3
2tan30°/1-tan230° = 2(1/√3)/1-(1/√3)2
= (2/√3)/(1-1/3) = (2/√3)/(2/3) = √3 = tan 60°
Hence , Correct answer is (C).
Ex 8.2 Question 3.
If tan (A + B) = √3 and tan (A – B) = 1/√3 ,0° < A + B ≤ 90°; A > B, find A and B.
Solution:
Ex 8.2 Question 4.
State whether the following are true or false. Justify your answer.
(i) sin (A + B) = sin A + sin B.
(ii) The value of sin θ increases as θ increases.
(iii) The value of cos θ increases as θ increases.
(iv) sin θ = cos θ for all values of θ.
(v) cot A is not defined for A = 0°.
Solution:
