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Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


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Ex 3.3, 4 Prove that 2sin2 3π/4 + 2cos2 π/4 + 2sec2 π/3 = 10 Solving L.H.S 2sin2 3π/4 + 2cos2 π/4 + 2sec2 π/3 Putting π = 180° 2 sin2 (3 × 180/4 ) + 2cos2 (180/4) + 2sec2 (180/3) = 2sin2 (135°) + 2 cos2 (45°) + 2sec2(60°) Here, cos 45° = 1/√2 sec 60° = 1/cos⁡〖60°〗 = 1/(1/2) = 2 sin 135° = sin ( 180 – 45° ) = sin 45° = 1/√2 Putting values 2 sin2 (135°) +2 cos2 (45°) + 2sec2 (60°) = 2 × (𝟏/√𝟐)^𝟐 + 2 × (𝟏/√𝟐)^𝟐 + 2 × (2)2 = 2 [(1/√2)^2 " + " (1/√2)^2 " + 22" ] = 2 [ 1/2 + 1/2 + 4] = 2 [1 + 4] = 2 × 5 = 10 = R.H.S ∴ L.H.S. = R.H.S. Hence proved

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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.