The distance between the points A\left(sin{\theta},cos{\theta}\right)and B\left(cos{\theta},-sin{\theta}\right)

STUDY MATERIALS
COURSES
MORE
SUCCESS STORY
ADMISSION
STORE

Back

JEE ADVANCE

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

JEE MAIN

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

NEET

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

BITSAT

CLASS XI - XII

CLASS XI - XII

CBSE BOARD

CLASS IX

CLASS X

CLASS XI

CLASS XII

CLASS VI

CLASS VII

CLASS VIII

UP BOARD

CLASS IX
CLASS X
CLASS XI
CLASS XII

CLASS IX

CLASS X

CLASS XI

CLASS XII

CUET

CRASH COURSE

CRASH COURSE

Courses

CLASSROOM COURSES
ONLINE COURSES

ONLINE COURSES

More

Solution

Q.
The distance between the points $A (s i n θ, c o s θ) a n d B (c o s θ, - s i n θ) i s p$ . Identify the correct statements:

(i) The value of p is 2.
(ii) The value of p depends on the value of $θ$
(iii) The value of p is independent of $θ$ .
(iv) The value of p is $\sqrt{2} .$ .

Choose the correct option from the following:

1 (iii) and (iv)

2 (i) and (iii)

3 (ii) and (iv)

4 (ii) and (iii)

Ans.
(1)

Distance between the points A and B :

$p = \sqrt{(s i n θ - c o s θ)^{2} + (c o s θ + s i n θ)^{2}} \Rightarrow p = \sqrt{2 {s i n}^{2} θ + 2 {c o s}^{2} θ - 2 s i n θ c o s θ + 2 s i n θ c o s θ} \Rightarrow p = \sqrt{2 ({s i n}^{2} θ + {c o s}^{2} θ)} = \sqrt{2 \times 1} = \sqrt{2}$

Want Us to Email you About Special Offers & Updates?