sin 10° + sin 20° + sin 40° + sin 50º = sin 70° + sin 80°.
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Answered by
4
Step-by-step explanation:
L.H.S. = 2sin15cos5+2sin45cos5 [ using sin C+sin D= 2sin C+D/2 cos C-D/2 for sin10+sin20 & sin40+sin50]
= 2cos5 (sin15+sin45)
= 2cos5 (2sin30cos15) [ using sin C+sin D= 2sin C+D/2 cos C-D/2 ]
= 2cos5 (2 x 1/2 x cos15)
= 2cos5 cos15
R.H.S. = sin70+sin80
= 2sin75cos5 [ using sin C+sin D= 2sin C+D/2 cos C-D/2 ]
sin75 = sin(90-15) = cos 15
L.H.S = 2cos5 cos15
R.H.S. = 2cos15 cos5 [ since, sin75 = cos15 ]
Answered by
0
Answer:
Step-by-step explanation:
LHS=(sin10+sin50)+(sin20+sin40)
=(2sin 30cos 20)+(2sin 30cos 10)
=2sin 30(cos10+cos20)
=
=sin70+sin80=RHS
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