This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
It seems you have provided a new set of questions. Since there is no question numbered "7" in the image you just sent, I will solve the first question in Section B, which is question 1. SECTION B: THEORY 1. Given Tan A = 3. Find the value of: (i) Sin A (ii) Cos A (iii) Sec A (iv) Cosec A (v) Cot A (In Surd form) Step 1: Use the definition of A. Given A = 3. In a right-angled triangle, A = OppositeAdjacent. So, we can consider the Opposite side to be 3 units and the Adjacent side to be 1 unit. Step 2: Calculate the Hypotenuse using the Pythagorean theorem. Hypotenuse^2 = Opposite^2 + Adjacent^2 Hypotenuse^2 = 3^2 + 1^2 Hypotenuse^2 = 9 + 1 Hypotenuse^2 = 10 Hypotenuse = sqrt(10) Step 3: Find the values of the trigonometric ratios. (i) Sin A A = OppositeHypotenuse = (3)/(sqrt(10)) Rationalize the denominator: A = (3)/(sqrt(10)) × sqrt(10)sqrt(10) = 3sqrt(10)10 The final answer for Sin A is 3sqrt(10)10. (ii) Cos A A = AdjacentHypotenuse = (1)/(sqrt(10)) Rationalize the denominator: A = (1)/(sqrt(10)) × sqrt(10)sqrt(10) = sqrt(10)10 The final answer for Cos A is sqrt(10)10. (iii) Sec A A = (1)/( A) = HypotenuseAdjacent = sqrt(10)1 A = sqrt(10) The final answer for Sec A is sqrt(10). (iv) Cosec A A = (1)/( A) = HypotenuseOpposite = sqrt(10)3 The final answer for Cosec A is sqrt(10)3. (v) Cot A A = (1)/( A) = AdjacentOpposite = (1)/(3) The final answer for Cot A is (1)/(3).