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Q) From the top of a light house, the angles of depression of two ships on the opposite sides of it are observed to be a and ẞ. If the height of the light house be h metres and the line joining the ships passes through the foot of the light house, show that the […]
Q)Â An observer 1.5 m tall is 28.5 m away from a tower and the angle of elevation of the top of the tower from the eye of the observer is 45 degrees. What is the height of the tower? Ans:Â Step 1: Let’s draw a diagram for the given question: Let the tower be
Q)Â An observer 1.5 m tall is 28.5 m away from a 30 m high tower. Determine the angle of elevation of the top of the tower from the eye of the observer. Ans:Â Step 1: Let’s draw a diagram for the given question: Let the tower be AB and observer be CD. We need
Q. Divide the polynomial x3 – 3 x2 + 5 x – 3 by x2 – 2 Ans:Â 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 ∴
Solve the quadratic equation: 2x^2 – 7x + 3 = 0 Read More »
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
Q) In a school, there are two sections of class X. There are 40 students in the first section and 48 students in the second section. Determine the minimum number of books required for their class library so that they can be distributed equally among students of both sections. Ans: STEP-BY-STEP SOLUTION To get a