prove that cos10 cos30 cos50 cos70 =3/16
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Answer:
√3
/2 (cos10.cos50.cos70)
= \sqrt{3}/4
√3
/4 (2cos10.cos50).cos70
= \sqrt{3}/4
√3
/4 (cos60+cos40).cos70
= \sqrt{3}/8
√3
/8 (cos70+ 2cos40.cos70)
= \sqrt{3}/8
√3
/8 (cos70+ cos110+cos30)
= \sqrt{3}/8
√3
/8 (cos70 -cos70 + \sqrt{3}/2
√3
/2 )
=3/16
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