# Category Archives: School Learning

Evaluate the following limits: Question 1.  Solution: We know if  such that  exists, then  We have, =  =  = ex Question 2.  Solution: We have, =  = … Read More
Question 1. Express each of the following as the sum or difference of sines and cosines: (i) 2 sin 3θ cos θ Solution: By using… Read More
Question 11. In any ∆ABC, prove the following: a cos A + b cos B + c cos C = 2b sin A sin C.… Read More
Question 1. Find the equation of a line passing through the point (2, 3) and parallel to the line 3x – 4y + 5 =… Read More
Sum the following series to n terms: Question 1. 3 + 5 + 9 + 15 + 23 + . . . . n terms… Read More
Question 1. Find the discriminant of the following quadratic equations: (i) 2x2 – 5x + 3 = 0   Solution: Given quadratic equation: 2x2 – 5x… Read More
Question 1. Find the distance between the following pair of points: (i) (-6, 7) and (-1,-5) (ii) (a + b, b + c) and (a… Read More
Question 1. Sketch the following graphs: (i) y = 2 sin 2x Solution: To obtain this graph y = 2 sin 2x, First we draw… Read More
Question 1. Find the general solution of following equations: (i) sin θ = 1/2 Solution: We are given, => sin θ = 1/2 => sin… Read More
Prove that: Question 1.  sin2 72o – sin2 60o = (√5 – 1)/8 Solution: We have, L.H.S. = sin2 72o – sin2 60o = sin2… Read More
Question 11. A rail road curve is to be laid out on a circle. What radius should be used if the track is to change… Read More
Question 1. Find the degree measure corresponding to the following radian measures using π = 22/7: (i) 9π/5 Solution: We know that π radians =… Read More
Question 1. If cos θ = 4/5, find all other trigonometric ratios of angle θ.   Solution: We are given, cos θ = 4/5. So,… Read More
Prove that: Question 1. sin 5θ = 5sin θ – 20 sin3 θ + 16 sin5 θ Solution: We have, L.H.S. = sin 5θ =… Read More
As a Part of Society, communication with people around is very common, and not all communications include facts. Facts are the Universal truth that we… Read More