if A=90degree state that sinB+sinC=/2
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In a triangle if A = 90 deg, then B+C = 90 deg.
So Sin B = Cos C.
As angle 0< C < 90 1 < Cos C + Sin C < √2
let P = cos C + sin C
P² = 1 + 2 Sin C Cos C
= 1 + Sin 2 C
So 1 < P² < 2
Hence 1 < Sin B + Cos C < √2
So Sin B = Cos C.
As angle 0< C < 90 1 < Cos C + Sin C < √2
let P = cos C + sin C
P² = 1 + 2 Sin C Cos C
= 1 + Sin 2 C
So 1 < P² < 2
Hence 1 < Sin B + Cos C < √2
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