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Byju's Answer
Standard XII
Mathematics
Sin(A+B)Sin(A-B)
Prove that: ...
Question
Prove that:
sin
10
∘
sin
50
∘
sin
60
∘
sin
70
∘
=
√
3
16
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Solution
We know that
4
s
i
n
θ
s
i
n
(
60
0
+
θ
)
s
i
n
(
60
0
−
θ
)
=
s
i
n
3
θ
So,
s
i
n
10
o
s
i
n
70
o
s
i
n
50
o
s
i
n
60
o
=
1
4
s
i
n
(
10
×
3
)
0
×
sin
60
o
=
√
3
16
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Similar questions
Q.
Prove that:
(i) cos 10° cos 30° cos 50° cos 70° =
3
16
(ii) cos 40° cos 80° cos 160° =
-
1
8
(iii) sin 20° sin 40° sin 80° =
3
8
(iv) cos 20° cos 40° cos 80° =
1
8
(v) tan 20° tan 40° tan 60° tan 80° = 3
(vi) tan 20° tan 30° tan 40° tan 80° = 1
(vii) sin 10° sin 50° sin 60° sin 70° =
3
16
(viii) sin 20° sin 40° sin 60° sin 80° =
3
16
Q.
The value of sin 50° − sin 70° + sin 10° is equal to
(a) 1
(b) 0
(c) 1/2
(d) 2
Q.
Prove that:
(i) cos 55° + cos 65° + cos 175° = 0
(ii) sin 50° − sin 70° + sin 10° = 0
(iii) cos 80° + cos 40° − cos 20° = 0
(iv) cos 20° + cos 100° + cos 140° = 0
(v)
sin
5
π
18
-
cos
4
π
9
=
3
sin
π
9
(vi)
cos
π
12
-
sin
π
12
=
1
2
(vii) sin 80° − cos 70° = cos 50°
(viii) sin 51° + cos 81° = cos 21°
Q.
Sin10°Sin50°Sin60°Sin70°=√3/16
Prove it
Q.
Prove that sin10+sin 30+sin 50+sin 70 =root3÷16
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Sin(A+B)Sin(A-B)
Standard XII Mathematics
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