The value of the expression [(sin 2 ⁡22 ° + sin 2 ⁡68 ° )/(cos 2 ⁡ 22 ° + cos 2 ⁡ 68 ° ) + sin 2 ⁡ 63 ° + cos⁡ 63 ° sin⁡27 ° ] is

(A) 3  (B) 2  (C) 1  (D) 0

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  1. Chapter 8 Class 10 Introduction to Trignometry (Term 1)
  2. Serial order wise

Transcript

Question 14 The value of the expression [(sin^2⁡22"°" + sin^2⁡68"°" )/(cos^2⁡〖22"°" 〗+ cos^2⁡68"°" )+sin^2⁡〖63"°" +cos⁡〖63"°" sin⁡27"°" 〗 〗 ] is (A) 3 (B) 2 (C) 1 (D) 0 (sin^2⁡22"°" + sin^2⁡68"°" )/(cos^2⁡〖22"°" 〗+ cos^2⁡68"°" )+sin^2⁡〖63"°" +cos⁡63"°" 𝒔𝒊𝒏⁡𝟐𝟕"°" 〗 Using sin θ = cos (90° − θ) = (sin^2⁡22"°" + sin^2⁡68"°" )/(cos^2⁡〖22"°" 〗+ cos^2⁡68"°" )+sin^2⁡〖63"°" +cos⁡〖63"°" 𝐜𝐨𝐬⁡〖(𝟗𝟎°−𝟐𝟕"°)" 〗 〗 〗 = (sin^2⁡22"°" + sin^2⁡68"°" )/(cos^2⁡〖22"°" 〗+ cos^2⁡68"°" )+sin^2⁡〖63"°" +cos⁡〖63"°" 𝒄𝒐𝒔⁡〖𝟔𝟑°〗 〗 〗 = (sin^2⁡22"°" + sin^2⁡68"°" )/(cos^2⁡〖22"°" 〗+ cos^2⁡68"°" )+〖𝒔𝒊𝒏〗^𝟐⁡〖𝟔𝟑"°" +〖𝒄𝒐𝒔〗^𝟐⁡𝟔𝟑"°" 〗 Using cos2 θ + sin2 θ = 1 (sin^2⁡22"°" + 〖𝒔𝒊𝒏〗^𝟐⁡𝟔𝟖"°" )/(cos^2⁡〖22"°" 〗+ 〖𝒄𝒐𝒔〗^𝟐⁡𝟔𝟖"°" )+1 = (sin^2⁡22"°" + 〖𝒄𝒐𝒔〗^𝟐⁡(𝟗𝟎° − 𝟔𝟖"°" ))/(cos^2⁡〖22"°" 〗+ 〖𝒔𝒊𝒏〗^𝟐⁡(𝟗𝟎° − 𝟔𝟖"°" ) )+1 = (sin^2⁡22"°" + 〖𝒄𝒐𝒔〗^𝟐⁡𝟐𝟐"°" )/(cos^2⁡〖22"°" 〗+ 〖𝒄𝒐𝒔〗^𝟐⁡𝟐𝟐"°" )+1 = 1+1 = 2 So, the correct answer is (B)

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.