Math, asked by kothasaritha19091985, 1 month ago

cos square 36+sin square 18​

Answers

Answered by shauryakumarjha256
0

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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