# Tutor profile: Vaibhav S.

## Questions

### Subject: Trigonometry

Solve the trigonometric equation given by (2sin(x) - 1)(tan(x) - 1) = 0 for 0 ≤ x ≤ 2 pi

The given equation is already factored (2sin(x) - 1)(tan(x) - 1) = 0 which means 2sin(x) - 1 = 0 or tan(x) - 1 = 0 sin(x) = 1/2 or tan(x) = 1 equivalent equations to the above solutions: x = pi/6, 5pi/6, x = pi/4 and x = 5pi/4

### Subject: Geometry

Find the relation between x and y if the points A(x, y), B(-5, 7) and C(-4, 5) are collinear ?

If ABC is col-linear , the area of triangle is zero. Therefore, 1/2[X1(Y2-Y3)+X2(Y3-Y1)+X3(Y1-Y2)]=0 =>1/2[X(7-5)+(-5)(5-Y)+(-4)(Y-7)] (Use BODMAS rule while opening brackets) 2x-25+5y-4y+28=0 => Required relation between X & Y is 2x+y+3=0

### Subject: Basic Math

The sum of the 4th and 8th terms of an AP is 24 and the sum of the 6th and 10th term is 44. Find the first three terms of the AP.

Given that sum of the 4th and 8th terms of an AP is 24. Let us assume a= first term; d= common difference. Applying the formula, A(n)=a +(n-1)d As given the condition; ⟹ a + 3d + a + 7d = 24 ⟹ 2a + 10d = 24 ...(i) Also the sum of the 6th and 10th term is 44. ⟹ a + 5d + a + 9d = 44 ⟹ 2a + 14d = 44 ...(ii) Subtracting equation (i) from equation (ii), we get: 4d = 20 ⟹ d = 5 Now we have got the "d",, let us find out "a" Substituting d = 5 in equation (i), we have: 2a + 10d = 24 ⟹ 2a + 10 (5) = 24 ⟹ 2a + 50 = 24 ⟹ 2a = −26 ⟹ a = −13 Hence first term of given A.P. is −13 and common difference is 5.

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