cos square 36+sin square 18
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Step-by-step explanation:
Firstly find out the value of sin(18°)sin(18°) using the compound angle formulae as shown.
cos(36°)=sin(90°−36°)=sin(54°)cos(36°)=sin(90°−36°)=sin(54°)
⇒cos(2×18°)=sin(3×18°)⇒cos(2×18°)=sin(3×18°)
⇒1−2sin2(18°)=3sin(18°)−4sin3(18°)⇒1−2sin2(18°)=3sin(18°)−4sin3(18°)
⇒4sin3(18°)−2sin2(18°)−3sin(18°)+1=0⇒4sin3(18°)−2sin2(18°)−3sin(18°)+1=0
Let x=sin(18°)x=sin(18°)
⇒4x3−2x2−3x+1=0⇒4x3−2x2−3x+1=0
⇒(x−1)(4x2+2x−1)=0⇒(x−1)(4x2+2x−1)=0
⇒x=1,x=5–√−14⇒x=1,x=5−14 or x=−5–√−14
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