Q) Evaluate: (2𝑠𝑖𝑛 2 600 − 𝑡𝑎𝑛 2 300) / 𝑠𝑒𝑐2 450 Ans: We know that: sin 600 = ; tan 300 = ; sec 450 = By submitting these values in the given expression, we get: = = = = = Please do press “Heart” button if you liked the solution.
September 2024
Q) Find the point(s) on the x-axis which is at a distance of √41 units from the point (8, -5). Ans: Let the point be A and coordinates of this point be (x, y) Since any point on X-axis will have y = 0, Hence, the coordinates of the point A will be (X, 0)
Q) Show that the points A(-5,6), B(3, 0) and C( 9, 8) are the vertices of an isosceles triangle. Ans: For a triangle to be an isosceles triangle, its any 2 sides should be equal. Let’s start by calculating length of its sides: We know that the distance between two points P (X1, Y1) and
Q) In 𝛥ABC, D, E and F are midpoints of BC,CA and AB respectively. Prove that △ 𝐹𝐵𝐷 ∼ △ DEF and △ DEF ∼ △ ABC Ans: (i): Prove that △ 𝐹𝐵𝐷 ∼ △ DEF: Let’s start from comparing triangles △ FBD and △ DEF. Since by midpoint theorem, The line segment in a
Q) In 𝛥ABC, P and Q are points on AB and AC respectively such that PQ is parallel to BC. Prove that the median AD drawn from A on BC bisects PQ. Ans: Step 1: Let’s start from comparing triangles △ APR and △ ABD. Here we have: ∠ APR = ∠ ABD (corresponding
In 𝛥ABC, P and Q are points on AB and AC respectively such that PQ is parallel to BC. Read More »
Q) If 𝛼 and β are zeroes of a polynomial 6 x2 – 5 x + 1, then form a quadratic polynomial whose zeroes are 𝛼2 and 𝛽2 . Ans: Step 1: Given polynomial equation 6 x2 – 5 x + 1 = 0 Comparing with standard polynomial, ax2 + b x + c =
Q) The sum of two numbers is 18 and the sum of their reciprocals is 9/40. Find the numbers. Ans: Let the numbers be X and Y Step 1: By first condition: X + Y = 18 ………… (i) Step 2: By second condition: ∴ ∴ 40 (Y + X) = 9 X Y e
The sum of two numbers is 18 and the sum of their reciprocals is 9/40. Find the numbers. Read More »
Q) If cosθ + sin θ = 1 , then prove that cosθ – sinθ = ±1 Ans: VIDEO SOLUTION STEL BY STEP SOLUTION Given that If cosθ + sinθ = 1 Step 1: We square the above equation on both sides, we get: (cos θ + sin θ) = (1) ∴ cos2 θ + sin2
If cosθ + sinθ = 1 , then prove that cosθ – sinθ = ±1 Read More »
Q) The minute hand of a wall clock is 18 cm long. Find the area of the face of the clock described by the minute hand in 35 minutes. Ans: ∵ Angle subtended by minute hand in full one hour or 60 mins = 3600 ∴ Angle subtended by minute hand in 35 mins =
Q) Prove that the lengths of tangents drawn from an external point to a circle are equal. Using above result, find the length BC of Δ ABC. Given that, a circle is inscribed in Δ ABC touching the sides AB, BC and CA at R, P and Q respectively and AB= 10 cm, AQ= 7cm
Prove that the lengths of tangents drawn from an external point to a circle are equal. Read More »