Question
If sin θ + cos θ = 1.2, find the value of sin θ. cos
θ.Solution
We know: sin² θ + cos² θ = 1 (Pythagoras identity). Given: sin θ + cos θ = 1.2. Let sin θ = x and cos θ = y. Then: x + y = 1.2, and x² + y² = ? Using the identity: (x + y)² = x² + y² + 2xy. 1.2² = x² + y² + 2xy. 1.44 = x² + y² + 2xy. From the Pythagoras identity: x² + y² = 1. Substitute into the equation: 1.44 = 1 + 2xy. 2xy = 1.44 - 1 = 0.44. xy = 0.44/2 = 0.22
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- What approximate value will come in place of the question mark (?) in the following question? (Note: You are not expected to calculate the exact value.)
- What approximate value will come in place of the question mark (?) in the following question? (Note: You are not expected to calculate the exactvalue.)
(1800.23 ÷ 29.98) + (816.32 ÷ 23.9) + 1634.11 = ?
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36.05 × 5.02 + 12.052 = ? + 9.09 × 4.04Â
(31.9)3 + (34.021)² - (16.11)3 - (42.98)² = ?
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