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Byju's Answer
Standard X
Mathematics
Standard Values of Trigonometric Ratios
Without using...
Question
Without using trigonometric tables prove
sin
40
o
−
cos
70
o
=
√
3
cos
80
o
.
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Solution
sin
40
0
−
cos
(
40
0
+
30
0
)
sin
40
0
−
[
cos
40
0
⋅
cos
30
0
−
sin
40
0
⋅
sin
30
0
]
[
sin
40
0
−
cos
40
0
⋅
√
3
2
+
sin
40
0
⋅
1
2
]
[
3
2
sin
40
0
−
cos
40
0
⋅
√
3
2
]
√
3
[
√
3
2
sin
40
0
−
cos
40
0
⋅
1
2
]
√
3
[
sin
60
0
⋅
sin
40
0
−
cos
40
0
⋅
cos
40
0
]
√
3
[
−
cos
(
40
0
+
60
0
)
]
√
3
[
−
cos
100
0
]
√
3
[
cos
(
180
0
−
100
0
)
]
√
3
cos
80
0
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