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Byju's Answer
Standard X
Mathematics
Complementary Trigonometric Ratios
Evaluate the ...
Question
Evaluate the following :
c
o
s
37
∘
s
i
n
53
∘
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Solution
We have,
c
o
s
37
∘
s
i
n
53
∘
=
c
o
s
(
90
∘
−
53
∘
)
s
i
n
53
∘
=
s
i
n
53
∘
s
i
n
53
∘
=
1
[
∵
c
o
s
(
90
∘
−
θ
)
=
s
i
n
θ
]
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0
Similar questions
Q.
Simplify
cos
37
∘
sin
53
∘
×
sin
18
∘
cos
72
∘
Q.
Without using tables, evaluate:
(i) sin
53
∘
÷
c
o
s
37
∘
(ii) cos
49
∘
÷
s
i
n
41
∘
(iii) tan
66
∘
÷
c
o
t
24
∘
Q.
Without using trigonometric tables, evaluate:
(i)
sin
26
°
cos
64
°
(ii)
sec
11
°
cosec
79
°
(iii)
tan
65
°
cot
25
°
(iv)
cos
37
°
sin
53
°
(v)
cosec
42
°
sec
48
°
(vi)
cot
34
°
tan
56
°
Q.
Without using trigonometric tables, prove that:
(i) sin53° cos37° + cos53° sin37° = 1
(ii) cos54° cos36° − sin54° sin36° = 0
(iii) sec70° sin20° + cos20° cosec70° = 2
(iv) sin35° sin55° − cos35° cos55° = 0
(v) (sin72° + cos18°)(sin72° − cos18°) = 0
(vi) tan48° tan23° tan42° tan67° = 1
Q.
Without using trigonometric tables, prove that:
(i) sin53° cos37° + cos53° sin37° = 1
(ii) cos54° cos36° − sin54° sin36° = 0
(iii) sec70° sin20° + cos20° cosec70° = 2
(iv) tan 15° tan 60° tan 75° =
3
(v) tan48° tan23° tan42° tan67° tan 45° = 1
(vi) (sin72° + cos18°)(sin72° − cos18°) = 0
(vii) cosec 39° cos 51° + tan 21° cot 69° – sec
2
21° = 0
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