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Trigonometric ratios and identities...these two questions in the image...please help

Trigonometric ratios and identities...these two questions in the image...please help

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Grade:11

1 Answers

Faiz
107 Points
5 years ago
19. (x + z) / 2 = y as x, y, z are in APUsing identities sinC - sinD in numerator and cos C - cosD in denominator, the expression becomes:Numerator: 2 cos[ (x + z) / 2 ] sin[ (x - z) / 2 ]Denominator: 2 sin[ (x + z) / 2 ] sin[ (x - z) / 2 ]Replace (x+z)/2 by y and divide them as 2 and sin[ (x - z) / 2 cancel out leaving behind cot yAns: cot y20. Let the given expression be equal to k.x= k cos py= k cos (p - 2π/3)z= k cos (p + 2π/3)Adding all:x+y+z = k[ cos p + cos (p - 2π/3) + cos (p + 2π/3) ]Using cosC + cosDx+y+z = k[ cos p + 2 cos p cos 2π/3 ]x+y+z = k[ cos p + 2 cos p (-1/2) ]x+y+z = k[ cos p - cos p]Ans: x+y+z = 0

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