Question

Formulate sets of your choice, involving algebraic and geometrical ideas.

Answer 1

(1)A = Set of all quadrilaterals

A = { Triangle, rectangle, Square...}

(2) B = Set of traingles

B = { Equilateral triangle, Scalene triangle, Acute angled triangle....}

(3) C = { x : x = Multiples of 2 }

C = { 2,4,6... }

(4) D = { x : x = 3n+1, n belongs to N and n<4}

D = { 4,7,10}

:)

Answer 2

Answer:

Step-by-step explanation:

=> {cosθ(1 + sinθ) + cosθ(1 - sinθ)}/(1 - sinθ)(1 + sinθ) = 4

=> {cosθ + cosθ.sinθ + cosθ - cosθ.sinθ}/(1 - sin²θ) = 4

=> 2cosθ/cos²θ = 4 [ we know, sin²x + cos²x = 1 so, (1 - sin²θ) = cos²θ]

=> 2/cosθ = 4

=> cosθ = 1/2 = cos60°

hence, in 0 < θ < 90° , θ = 60°

now, if given equation is not defined.

(1 - sinθ) = 0

in 0 < θ < 90° , sinθ = 1 at 90°

hence, equation is undefined at θ = 90°

[ note : one more case for undefined, (1 + sinθ) = 0 , but in 0 < θ < 90° it's not possible. thars why I didn't mention it above]