Advanced Mathematics: Trigonometry Question

Dim Ray

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Hi! kwa members wote wa JF

Straight to the point kuna haya maswali naomba msaada

1. Find CotB if CosA=1/4 and Cos(A-B)=8
2. Express CosecX+Cosec2X+Cosec4X as the difference of two Cotangents natanguliza shukurani zangu

Stay Safe Corona ain't a doll to play with
 
mimi nili "expand" Cos(A-B) na kuingizia value za Cos A na Sin A halafu kwa kuwa tunamtafuta Cot B nika form hii equation ingine Sin²B+Cos²B=1 halafu nika let Sin B=X na Cos B=Y.

Resulting equations zikawa hizi

X²+Y²=1..........(i)
X+√(15)Y=32.....(ii)
Hapo nime assume angle A ipo kwenye first quadrant, shida ni kwamba jibu linakuja in terms of Complex number 😰
 
jibu ni 12/31 sasa kulipata ndo shida.

maana angle A ina fit quadrant ya kwanza na ya nne
Nadhani this is the way

Value ya Cos A = 1/4 na Sin A = √15/4
Cot B = Cos B/ Sin B

Cos(A-B)=CosACosB + SinASinB
8=(1/4)CosB + (√15/4)SinB ~Divide by Sin B both sides
8/ SinB=(1/4)CosB/SinB + (√15/4)SinB/SinB
8/Sin B= CotB/4 + √15/4 ~Times by 4 both Sides

32SinB =Cot B + √15
Cot B = 32Sin B - √15

Haya Sin B tunaipataje tuiweke hapo
[emoji38][emoji38][emoji38][emoji38]
 
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