Q) prove that sin 6 θ + cos 6 θ = 1 – 3 sin 2 θ cos 2 θ Ans: Let’s start from LHS LHS = prove that sin 6 θ + cos 6 θ = (sin 2 θ) 3 + (cos 2 θ) 3 We know that a 3 + b 3 = (a + b) (a […]
prove that sin 6 θ + cos 6 θ = 1 – 3 sin 2 θ cos 2 θ Read More »
July 2024
Q) The angle of elevation of an aircraft from a point A on the ground is 60°. After a flight of 30 seconds, the angle of elevation changes to 30°. The aircraft is flying at a constant height of 3500√3 m at a uniform speed. Find the speed of the aircraft. Ans: Let’s start with the
Q) If the length of a rectangle is reduced by 5 cm and its breadth is increased by 2 cm, then the area of the rectangle is reduced by 80 cm². However, if we increase the length by 10 cm and decrease the breadth by 5 cm, its area is increased by 50 cm². Find
If the length of a rectangle is reduced by 5 cm and its breadth is increased by 2 cm, Read More »
Q) Can the number (15n), n being a natural number, end with the digit 0 ? Ans: For any number to end with the digit 0, it will be divisible by 10 Since 10 = 2 x 5, therefore, a number ending with digit 0 will be divisible by 2 and 5 both. Next, since
Can the number (15n), n being a natural number, end with the digit 0? Give reasons. Read More »
Q) 22. Find the type of triangle ABC formed whose vertices are A(1, 0), B(-5, 0) and C(-2, 5). Ans: Step 1: Let’s plot the points on the graph: Step 2: Given vertices are A(1, 0), B(- 5, 0) and C(- 2, 5). Let’s find out lengths of all the sides: We know that the
Find the type of triangle ABC formed whose vertices are A(1, 0), B(-5, 0) and C(-2, 5). Read More »
Q) If 2 sin (A + B) = √3 and cos (A – B) = 1 , then find the measures of angles A and B. 0 <= A B, (A + B) <= 90 deg Ans: Let’s take each of the given values one by one: 2 sin(A + B) = √3 ∴ sin (A
Q) Evaluate: 2 sin2 300 sec 600 + tan2 600 Ans: We need to find the value of: 2 sin2 300 sec 600 + tan2 600 We know that sin 300 = , sec 600 = 2, tan 600 = √3 by substituting these values in the given expression, we get: 2 sin2 300 sec 600 + tan2 600 = 2 (
Q) In the given figure, AB and CD are tangents to a circle centred at O. Is angle BAC = angle DCA ? Justify your answer. Ans: Step 1: Let’s connect center O with points A and C Step 2: Since BA is the tangent to the circle and OA is the radius of the
Q) In what ratio is the line segment joining the points (3, – 5) and (- 1, 6) divided by the line y = x ? Ans: Method 1: Step 1: Now, by section formula, coordinates of point P (X, Y) which lies between two points (x1, y1), (x2, y2) will be given by: P (X,Y)
Q) A(3, 0), B(6, 4) and C(-1, 3) are vertices of a triangle ABC. Find length of its median BE. Ans: Let’s plot the points on the graph: Step 1: To draw median BE, point E lies on AC Let’s consider the coordinates of E are (x, y) Since E is the midpoint of A C, we