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If SecA = x + 1/4x , Then prove that SecA + TanA = 2x or 1/2x
If SecA = x + 1/4x , Then prove that SecA + TanA = 2x or 1/2x SecA = x +1/4x ∴, Sec²A = (x+1/4x)² = x² + 2.x.1/4x + 1/16x² = x² + 1/2 + 1/16x² Now, Sec²A - Tan²A = 1 ⇒ Tan²A = Sec²A - 1 ⇒ T an²A = x² + 1/2 + 1/16x² - 1 ⇒ T an²A = x² + 1/16x² - 1/2 ⇒ T an²A = x² - 2.x.1/4x + 1/16x² ⇒ T an²A = (x-1/4x)² ⇒ T anA = ± (x-1/4x) ∴ CASE 1: T anA = x - 1/4x S ecA + T anA = x + 1/4x + x -1/4x = 2x CASE 2: T anA = -(x - 1/4x) SecA + T anA = x + 1/4x - ( x - 1/4x ) = x + 1/4x - x + 1/4x = 1/4x + 1/4x = 2/4x = 1/2x (Proved)
The measure of length and breadth of a rectangle are l = (30.0 ± 0.2) cm and b = (10.0 ± 0.1) cm. What is the percentage error in the calculation of area of rectangle?
The measure of length and breadth of a rectangle are l = (30.0 ± 0.2) cm and b = (10.0 ± 0.1) cm. What is the percentage error in the calculation of area of rectangle? Length = 30.0 ± 0.2 cm Breadth = 10.0 ± 0.1 cm Area = Length × Breadth = (30.0 × 10.0) = 19.38 cm² ΔA = A × (ΔL/L + ΔB/B) = 300.00 × (0.2/30.0 + 0.1/10.0) = 5 cm² Area of rectangle = (300.00 ± 5.0) cm² percentage error in the calculation of area of rectangle = ΔA/A × 100 = 5/300 × 100 = 1.67%
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