EXERCISE 8.2
Q.4) State whether the following are true or false. Justify your answer.
(i) sin (A + B) = sin A + sin B
Justification:
Let A = 30º,
B = 60º
sin (A + B)
sin
=
=
sin 90º
=
1
sin A
+
sin B
=
sin 30º
+
sin 60º
=
2
+
2
=
2
sin (A + B) ≠ sin A + sin B
∴
1
(30º
+
90º)
Hence, the given statement is false.
when A = 30º, B = 60º
EXERCISE 8.2
Q.4) State whether the following are true or false. Justify your answer.
(ii) The value of sin θ increases as θ increases.
Justification:
sin 0º
=
0
sin 30º
=
1
2
= 0.5
sin 45º
=
1
=
2
=
2
1.41
0.7
=
sin 60º
=
2
=
2
1.73
0.87
=
sin 90º
=
1
∴
The value of sin θ increases as θ increases from 0º to 90º.
Hence, the given statement is true.
(Approx.)
(Approx.)
EXERCISE 8.2
Q.4) State whether the following are true or false. Justify your answer.
(iii) The value of cos θ increases as θ increases.
Justification:
cos 0º
=
1
cos 30º
=
2
cos 45º
=
1
0.7
=
cos 60º
=
2
0.5
=
cos 90º
=
0
∴
Hence, the given statement is false.
1
=
2
1.73
0.87
=
2
=
1.41
2
=
(Approx.)
(Approx.)
EXERCISE 8.2
Q.4) State whether the following are true or false. Justify your answer.
(iv) sin θ = cos θ for all values of θ.
Justification:
30º,
If θ
=
sin 30º
=
2
1
cos 30º
=
2
cos 30º
∴
sin 30º
≠
sin θ ≠ cos θ , when θ = 30º
∴
∴
Hence, the given statement is false.
EXERCISE 8.2
Q.4) State whether the following are true or false. Justify your answer.
(v) cot A is not defined for A = 0º.
Justification:
cot 0º
=
sin 0º
=
cot A is not defined.
cos 0º
1
0
∴
1
0
is not defined.
Hence, the given statement is true.