Q) Prove that sec A (1- sin A)(sec A + tan A) = 1 Ans: Let’s start from LHS LHS = sec A (1- sin A)(sec A + tan A) = = = We know that sin2A + cos2A = 1 or we can say that, 1 – sin2A = cos2A LHS = = 1 ……….. […]
Prove that sec A (1- sin A)(sec A + tan A) = 1 Read More »
Q) Prove that Ans: Let’s start from LHS LHS = = = We know that sin2A + cos2A = 1 LHS = = =tan A …….. RHS Hence proved!
Prove that: (sin A – 2 sin^3 A)/(2cos^3 A – cos A) = tan A Read More »
Q) Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line segment joining the points of contacts at the centre. Ans: Let’s draw a diagram with a circle of radius r and O as centre. Let the two tangents RP
Q) Prove that √5 is an irrational number. Ans: Let us assume that √5 is a rational number Let √5 = ; where q ≠ 0 and let p, q are co-primes. 5q2 = p2………………. (i) It means p2 is divisible by 5 p is divisible by 5 Hence, we can write that p = 5a,
Prove that root 5 is an irrational number. Read More »
Q) Which term of the A.P. : 65, 61, 57, 53,………… is the first negative term. Ans: This is A.P. of decreasing order. In the given A.P., we can see that: First term a = 65 and common difference d = -4 Let first negative term be nth term, say Tn We know that nth
Which term of the A.P. : 65, 61, 57, 53,………… is the first negative term. Read More »
Q) How many terms are there in an A.P. whose first and fifth terms are -14 and 2, respectively and the last term is 62. Ans: Let’s consider an A.P with first term as N1 and common difference as ‘d’. Next, we know that nth term of an A.P. = a + (n-1) d
Q) If A and B are acute angles such that sin(A-B) = 0 and 2 cos (A+B) -1 = 0, then find angles A and B. Ans: Given that sin(A – B) = 0 Since we know that, sin 00 = 0 A – B = 0 ……….. (i)
Q) Evaluate Ans: Since sin2θ + cos2θ = 1 = = 5 cos2 60 + 4 sec2 30 – tan2 45 = = = =
Evaluate (5cos^2 60 + 4 sec^2 30 – tan ^2 45) / (sin^2 30 + cos^2 30) = 1 + sin θ cos θ Read More »
Q) If a fair coin is tossed twice, find the probability of getting ‘at most one head’. Ans: When we toss 2 fair coins, here are the possible outcomes: HH, HT, TH, TT Here, we need to get at most 1 head. It means we will include outcomes of getting 1 head and no head. Since
If a fair coin is tossed twice, find the probability of getting ‘at most one head’. Read More »
Q) Find the sum and product of the roots of the quadratic equation 2×2 – 9x + 4 = 0. Ans: We know that sum of roots (α + β) = Sum of roots = = Next, we know that the product of the roots (α x β) = Product of the roots
Find the sum and product of the roots of the quadratic equation 2x^2 – 9 x + 4 = 0. Read More »