Question

The distance between the points (a cos A, 0) and ( 0, a sin A) is

a
a^2
1
0​

Answer 1

Answer:

a

Step-by-step explanation:

$\red{\boxed{\rm Solution}}$

Let P1 be (acosA , 0) and P2 be (0 , asinA)

Therefore,

x1 = acosA, x2 = 0

y1 = 0, y2 = asinA

We know that distance between two points of co-ordinates (x1, y1) and (x2, y2) is given by the formula

$\rm D \: = \: \sqrt{(x_2-x_1)^{2} + (y_2-y_1)^2}$

Using the above formula,

$\rm \to \: \sqrt{ {(0 - acosA) }^{2} + (asinA - 0)² }$

$\rm \to \sqrt{(acosA)² + (asinA)²}$

$\rm \to \sqrt{a^{2} cos²A + a^{2} sin²A}$

$\rm \to \sqrt{a²(cos²A + sin²A)}$

As addition is commutative, i.e a + b = b + a

$\rm \to \sqrt{a²(sin²A + cos²A)}$

We know that sin²A + cos²A = 1

Using the above formula to simplify,

$\to \rm \sqrt{a²}$

We know that √n² = n as square and square root gets cancelled

$\to \rm \: a$