Check sibling questions

Given that sin θ = a/b, then cos θ is equal to

(A) b/√(b^2  - a^2 )   

(B) b/a  

(C) √(b^2  - a^2 )/b   

(D) a/√(b^2  - a^2 )



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Question 7 Given that sin θ = 𝑎/𝑏, then cos θ is equal to (A) 𝑏/√(𝑏^2 − 𝑎^2 ) (B) 𝑏/𝑎 (C) √(𝑏^2 − 𝑎^2 )/𝑏 (D) 𝑎/√(𝑏^2 − 𝑎^2 ) Now, cos2 θ = 1 − sin2 θ Putting sin θ = 𝑎/𝑏 cos2 θ = 1−(𝑎/𝑏)^2 cos2 θ = 1−𝑎^2/𝑏^2 cos2 θ = (𝒃^𝟐 − 𝒂^𝟐)/𝒃^𝟐 Taking square root cos θ = ± √((𝑏^2 − 𝑎^2)/𝑏^2 ) cos θ = ± √(𝑏^2 − 𝑎^2 )/𝑏 Since only positive values are given in options cos θ = √(𝒃^𝟐 − 𝒂^𝟐 )/𝒃 So, the correct answer is (C)

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.