Ex 3.3, 4 - Prove 2sin2 3pi/4 + 2cos2 pi/4 + 2sec2 pi/3 = 10 - Finding Value of trignometric functions, given angle

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Ex 3.3, 4 Prove that 2sin2 3π/4 + 2cos2 π/4 + 2sec2 π/3 = 10 Taking 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°) 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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