Math, asked by sanskriti27257, 8 months ago

sin 10° + sin 20° + sin 40° + sin 50º = sin 70° + sin 80°.​

Answers

Answered by bap1299bhartisharma
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 ZoopyZanas
0

Answer:

Step-by-step explanation:

LHS=(sin10+sin50)+(sin20+sin40)

=(2sin 30cos 20)+(2sin 30cos 10)

=2sin 30(cos10+cos20)

=2 . \frac{1}{2} (sin80+sin70)

=sin70+sin80=RHS

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