the value of sin 105 degree is
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Answered by
10
Answer:
sin (105) = sin (15 + 90) = cos 15
Answered by
0
Answer:
explanation
(
√
2
+
√
3
2
)
Explanation:
sin (105) = sin (15 + 90) = cos 15.
First find (cos 15). Call cos 15 = cos x
Apply the trig identity:
cos
2
x
=
2
cos
2
x
−
1
.
cos 2x = cos (30)
=
√
3
2
=
2
cos
2
x
−
1
2cos^2 x = 1 + sqrt3/2 = (2 + sqrt3)/2
cos^2 x = (2 + sqrt3)/4
cos x = cos 15 = (sqrt(2 + sqrt3)/2. (since cos 15 is positive)
sin
(
105
)
=
cos
(
15
)
=
√
2
+
√
3
2
.
Check by calculator.
sin (105) = cos 15 = 0.97
√
2
+
√
3
2
=
1.93
2
=
0.97
.
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