Ex 8.2, 2 (iv) (MCQ) - Chapter 8 Class 10 Introduction to Trignometry

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Ex 8.2, 2 Choose the correct option and justify your choice : (iv) (2 𝑡𝑎𝑛⁡〖30°〗)/(1 − tan^2⁡〖30°〗 ) (A) cos 60° (B) sin 60° (C) tan 60° (D) sin 30° We know that , tan "30°" = 𝟏/√𝟑 So, (2 tan⁡〖30°〗)/(1 − 𝑡𝑎𝑛2 30°) = (𝟐 × (𝟏/√𝟑))/(𝟏 − (𝟏/√𝟑)^𝟐 ) = (2/√3)/(1 − 1/3) = (2/√3)/(2/3) = 𝟐/√𝟑×𝟑/𝟐 = 2/√3×(√3 × √3)/2 = √𝟑 Options are (A) cos 60° (B) sin 60° (C) tan 60° (D) sin 30° Since tan "60°" =√𝟑 So, the correct answer is (c)