Question 4 Prove that 2(sin (3π / 4))^2 + 2(cos (π / 4))^2 + 2(sec (π / 3))^2 = 10
Class X1 - Maths -Trigonometric Functions Page 73
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LHS = 2sin²(3π/4) + 2cos²(π/4) + 2sec²(π/3)
= 2sin²(π -π/4) + 2cos²(π/4)+2sec²(π/3)
=2sin²(π/4) + 2cos²(π/4)+2sec²(π/3)
=2sin²(45°) + 2cos²(45°)+2sec²(60°)
= 2 × (1/√2)² + 2×(1/√2)² + 2×(2)²
= 1 + 1 + 8 = 10 = RHS
= 2sin²(π -π/4) + 2cos²(π/4)+2sec²(π/3)
=2sin²(π/4) + 2cos²(π/4)+2sec²(π/3)
=2sin²(45°) + 2cos²(45°)+2sec²(60°)
= 2 × (1/√2)² + 2×(1/√2)² + 2×(2)²
= 1 + 1 + 8 = 10 = RHS
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