Prove that sinº sin(60° – tita ) sin (60° +tita ) = 1/4sin3 tita, hence find the value of sin20°. sin40°. sin 80 °
Answers
Answered by
1
Answer:
sin20°sin40°sin60°sin80°
=sin(30−10)+sin(30+10)×
2
3
sin(90−10)
=
2
3
×(sin30cos10−sin10cos30)×(sin30cos10+sin10cos30)×(sin90cos10−sin10cos90)
=
2
3
×(sin
2
30cos
2
10−sin
2
10cos
2
30)×cos10
=
2
3
(cos
2
10×
4
1
−sin
2
10×
4
3
)×cos10
=
2
3
×(cos
2
10×
4
1
−(1−cos
2
10)×
4
3
)×cos10
=
2
3
×(
4
(cos
2
10)
−
4
3
+3
4
(cos
2
10)
)×cos10
=
2
3
×(cos
2
10−
4
3
)×cos10
=
2
3
×
4
(4cos
3
10−3cos10)
=
2
3
×cos30
=
8
3
×
2
3
=
16
3
=0.1875
Hence, the answer is 0.1875.
Hope it was helpful to you
Make me as brainliest
Similar questions