Q. Divide the polynomial x3 – 3 x2 + 5 x – 3 by x2 – 2 Ans: To divide the given polynomial, we can write the function as: = = = = = = = = = = = = Therefore, When we divide X3 – 3 X2 + 5 X – 3 by X2 […]
Divide the polynomial x³ – 3x² + 5x – 3 by x² – 2 Read More »
Q) Prove that: (1 + cot 2 θ) (1 – cos θ) (1 + cos θ) = 1 Ans: Method 1: Step 1: Let’s start with LHS and put values of cot θ: LHS = (1 + cot 2 θ) (1 – cos θ) (1 + cos θ) = (1 + ( [∵ (a – b)
Prove that: (1 + cot² θ) (1 – cos θ) (1 + cos θ) = 1 Read More »
Q. Solve the quadratic equation: 2 X^2 – 7 X + 3 = 0 Ans: Given equation is: 2 X ^2 – 7 X + 3 = 0 ∴ 2 X ^2 – 6 X – X + 3 = 0 ∴ 2 X (X – 3) – 1 (X – 3) = 0 ∴
Q) Prove that (2 + √3) / 5 is an irrational number. It is given that √3 is an irrational number. Ans: STEP BY STEP SOLUTION Let’s start by considering is a rational number. ∴ (here p and q are integers and q ≠ 0) ∴ ∴ ∴ Since p and q are integers,
Q) Prove that Ans: Method 1: Step 1: Let’s start with LHS and put values of cot A and tan A: LHS = = = Step 2: We know that sin 2 A + cos 2 A = 1 = = = Hence Proved ! Method 2: Let’s start with LHS and applying trigonometric
Prove that (1 + cot^2 A) / (1 + tan^2 A) = cot^2 A Read More »
Q) Prove that 1 + tan 2 A = sec 2 A Ans: Step 1: Let’s draw a right angled triangle: Here ABC is a triangle where ∠ B is right angle. Step 2: By applying Pythagoras theorem, we know: AB 2 + BC 2 = AC 2 Step 3: Let’s divide the above