Ex 8.2, 1 (v) - Chapter 8 Class 10 Introduction to Trignometry

Transcript

Ex 8.2, 1 Evaluate the following : "5 cos2 60° + 4 sec2 30° – tan2 45°" /"sin2 30° + cos2 30°" We know that cos "60° = " 1/2 sec "30° = " 1/cos⁡〖30°〗 "= " 2/√3 tan "45°" = 1 sin "30° = " 1/2 cos "30°" = √3/2 Now, (𝟓 𝒄𝒐𝒔𝟐 𝟔𝟎°+ 𝟒 𝒔𝒆𝒄𝟐 𝟑𝟎°−𝐭𝐚𝐧𝟐⁡〖𝟒𝟓°〗)/(𝒔𝒊𝒏𝟐 𝟑𝟎° + 𝒄𝒐𝒔𝟐 𝟑𝟎°) Putting values = (𝟓(𝟏/𝟐)^𝟐 + 𝟒(𝟐/√𝟑)^𝟐 − (𝟏)𝟐)/((𝟏/𝟐)^𝟐 + (√𝟑/𝟐)^𝟐 ) = (5/4 + 4 × ( 2 × 2)/(√3 × √3) − 1)/(1/4 + (√3 × √3)/(2 × 2)) = (𝟓/𝟒 + 𝟏𝟔/𝟑 − 𝟏)/(𝟏/𝟒 + 𝟑/𝟒) = ((5 × 3 + 16 × 4 − 1 × 4 × 3 )/(4 × 3) )/((1 + 3)/4 ) = ((15 + 64 − 12 )/(4 × 3) )/(4/4 ) = ((67 )/12 )/1 = 𝟔𝟕/𝟏𝟐 Hence, (𝟓 𝒄𝒐𝒔𝟐 𝟔𝟎°+ 𝟒 𝒔𝒆𝒄𝟐 𝟑𝟎°−𝐭𝐚𝐧𝟐⁡〖𝟒𝟓°〗)/(𝒔𝒊𝒏𝟐 𝟑𝟎° + 𝒄𝒐𝒔𝟐 𝟑𝟎°) = 𝟔𝟕/𝟏𝟐