Find the value of cos18∘

Question

Find the value of  cos18∘

Samantha Summers · Accepted Answer

Find the value of cos18°using multiple angle formulae of trigonometric ratios  Let angle A=18°  Thus, 5A=90°⇒2A+3A=90˚  ⇒2A=90˚-3A  Taking sin e on both sides, we get  sin2A=sin(90˚-3A)=cos3A⇒2sinA×cosA=4cos3A-3cosA⇒2sinA×cosA-4cos3A+3cosA=0  ⇒cosA(2sinA-4cos2A+3)=0Dividing both sides bycosA=cos18˚≠0, we get2sinA-4(1-sin2A)+3=0⇒4sin2A+2sinA-1=0, which is a quadratic equation in sinA  ⇒sinA=-2±22-44-124  =-2±16+48=-2±258⇒sinA=-1±54Now the value of cos18∘ is ⇒cos18∘=1-sin218∘  =1-5-142=1-5+1-2516=10+2516⇒cos18∘=10+254  Thus, the value of cos18∘=10+254

Find the value of cos18∘

Answered question

Answer & Explanation