All the stuff

Question 1

1 + tan²ϴ =

Answer 1

sec²ϴ

Question 2

1 + cot²ϴ =

Answer 2

cosec²ϴ

Question 3

Sin2ϴ

Answer 3

2sinϴcosϴ

Question 4

Cos2ϴ (to cos and sin)

Answer 4

Cos²ϴ - Sin²ϴ

Question 5

Cos2ϴ(to cos)

Answer 5

2Cos²ϴ - 1

Question 6

Cos2ϴ(to sin)

Answer 6

1 - 2Sin²ϴ

Question 7

Tan2ϴ

Answer 7

2Tanϴ / 1 - Tan²ϴ

Question 8

secϴ

Answer 8

1/cosϴ

Question 9

cosecϴ

Answer 9

1/sinϴ

Question 10

cotϴ

Answer 10

1/tanϴ = cosϴ/sinϴ

Question 11

Equation of line passing through (a1,a2,a3) in direction (u1,u2,u2) in vector form

Answer 11

r = (a1)………..(u1)
……(a2)+…..λ(u2)
……(a3)……….(u3)

Question 12

Equation of line passing through (a1,a2,a3) in direction (u1,u2,u2) Cartesian form

Answer 12

(x-a1)/u1 = (y-a2)/u2 = (z-a3)/u3

Question 13

angle between two vectors is given by

Answer 13

Cosθ = a.b / |a|.|b| 
|a| = sum of the xyz components squared and square rooted

Question 14

the Cartesian equation for a plane perpendicular to (n1) ……………………………………………………………………………………..(n2)
……………………………………………………………………………………..(n3)

Answer 14

(n1)X + (n2)Y + (n3)Z + d = 0

Question 15

the vector perpendicular to the plane (n1)X + (n2)Y + (n3)Z + d = 0

Answer 15

(n1)
(n2)
(n3)

Question 16

Distance of a point from a plane is found by

Answer 16

construct a line perpendicular to the plane and through the given point , find where the line intersects the plane, find the distance between the two points

Question 17

2 / (x+1)(x+2) in partial fractions

Answer 17

a/(x+1) + b/(x+2)

Question 18

2x + 1 / (x²+1)(x+2) in partial fractions

Answer 18

ax+b/(x²+1) + c/(x+2)

Question 19

2x + 1 / (x+1)²(x+2) in partial fractions

Answer 19

a/(x+1) + b/(x²+1) + c/(x+2)

Question 20

integrating partial fraction e.g 2 / (x+1)(x+2)

Answer 20

∫a/(x+1) + ∫b/(x+2)

Question 21

Differentiating parametric equation

Answer 21

(dy/dt) / (dx/dt)

Question 22

Volume rotated 360 about x axis

Answer 22

V = π ∫y² dx

Question 23

Volume rotated 360 about y axis

Answer 23

V = π ∫x² dy

Question 24

e.g dy/dx = 2x becomes

Answer 24

y = x² + c

Question 25

e to the power of a constant is given as

Answer 25

A