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

Last updated at April 16, 2024 by

Slide13.JPG

Slide14.JPG
Slide15.JPG

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

Ask a doubt
Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.