Ex 8.2

Chapter 8 Class 10 Introduction to Trignometry
Serial order wise

### Transcript

Ex 8.2, 1 Evaluate the following : (iii) "cos 45°" /"sec 30° + cosec 30°" We know that, "cos 45°" = 1/√2 "sec 30°" = 1/(cos⁡〖30°〗 ) = 1/(√3/2) = 𝟐/√𝟑 "cosec 30°" = 1/sin⁡〖30°〗 = 1/(1/2) = 2/1 = 2 Hence, 𝒄𝒐𝒔⁡〖𝟒𝟓°〗/(𝒔𝒆𝒄⁡〖𝟑𝟎°〗+ 𝒄𝒐𝒔𝒆𝒄 𝟑𝟎°) = (1/√2)/((2/√3 + 2/1) ) = 𝟏/√𝟐 × 𝟏/((𝟐/√𝟑 + 𝟐/𝟏) ) = 1/√2×1/((2 × 1 + 2 × √3)/(√3 × 1)) = 1/√2×(√3 × 1)/((2 × 1 + 2 × √3) ) = 𝟏/√𝟐×√𝟑/((𝟐 + 𝟐√𝟑) ) = (1 ×√3)/(√2 × 2(1 + √3) ) = √3/(2√2 (1 + √3) ) = √3/(2√2 (√3 + 1) ) Rationalizing = (√3 (√𝟑 − 𝟏))/(2 √2 (√𝟑 + 𝟏) (√𝟑 − 𝟏) ) We know that, (a + b) (a – b) = a2 – b2 Putting a = √3 , 𝑏=1 = (3 − √3)/(2√2 ((√3 )2 −12) ) = (3 − √3)/(2√2 (3 − 1)) = (𝟑 − √𝟑)/(𝟐√𝟐 × 𝟐) Multiplying √2 on numerator and denominator) = ((3 − √3 ))/(4√2 )× √2/√2 = (3√2 − √3 ×√2 )/(4 × 2) = (𝟑√𝟐 −√𝟔 )/𝟖 Hence, 𝒄𝒐𝒔⁡〖𝟒𝟓°〗/(𝒔𝒆𝒄⁡〖𝟑𝟎°〗+ 𝒄𝒐𝒔𝒆𝒄 𝟑𝟎°) = (𝟑√𝟐 −√𝟔 )/𝟖

#### 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.