Physical quantity x and y are related as y = 4 t a n x . If at x = π 4 radian error in measurement of x is 2 % then find % error in measurement of y at x = π 4 .

Step-by-step solution

d y d x = 4 s e c 2 x , Δ y y = 4 s e c 2 Δ x 4t a n x Δ y y × 100 = 4 s e c 2 x 4 t a n x × Δ x × 100 = 2 × Δ x × 100 Δ x x × 100 = 2 100 Δ x = 2 × π 4 = π 2 Δ y y × 100 = π 2