Exercise 8.2
(i)
Evaluate the following :
(i) sin 60° cos 30° + sin 30° cos 60°
=
=
=
=
=
(ii)
(ii) 2
=2
= 2 +
=
(iii)
(iii)
We know that cos 45° =
Substituting we get:
=
=
=
Multiplying numerator and denominator by
=
=
=
(iv)
(iv)
We know that sin 30° =
Substituting we get:
=
=
=
Multiplying numerator and denominator by
=
=
=
(v)
(v)
We know that sin 30° =
=
=
=
=
=
(i)
Answer the following :
(i)
Answer: sin
(ii)
(ii)
Answer:
(iii)
(iii) sin 2A = 2 sin A is true when A =
Answer:
(iv)
(iv)
Answer: tan
3. If tan (A + B) =
Solution:
Given that, tan (A + B) =
Since, tan
Therefore, tan (A + B) = tan 60°
(A + B) =
tan (A - B) = tan
(A - B) =
On adding both equations (i) and (ii), we obtain:
A + B + A - B =
A =
By substituting the value of A in equation (i) we obtain
A + B =
B = 60° - 45° =
Therefore, ∠A = 45° and ∠B = 15° (A
4. State whether the following are true or false. Justify your answer.
(i)
(i) sin (A + B) = sin A + sin B.
Answer:
Let A = 30° and B = 60°
L.H.S = sin (A + B)
= sin (30° +
= sin
=
R.H.S = sin A + sin B
= sin 30° + sin 60°
=
=
Since, sin (A + B)
Hence, the given statement is false.
(ii)
(ii) The value of sin θ increases from 0 to 1 as θ increases from 0° to 90°.
Answer:
sin 0° =
sin 30° =
sin 45° =
sin 60° =
sin 90° =
Hence, the given statement is true.
(iii)
(iii) The value of cos θ decreases from 1 to 0 as θ increases from 0° to 90°
Answer:
cos 0° =
cos 30° =
cos 45° =
cos 60° =
cos 90° =
Hence, the given statement is false.
(iv)
(iv) sin θ = cos θ for all values of θ, this is true when θ = 45°
Answer:
As sin 45° =
It is not true for other values of θ
sin
sin
sin 90° =
Hence, the given statement is false.
(v)
(v) cot A =
Answer:
cot 0° =
Hence, the given statement is true.