Find the value of the following:|x|

Question

Find the value of the following:|x|<1, y<0 and xy < 1.ORProve that:

Philoid · Accepted Answer

Given:

Here, we use some trigonometric formulas:

…(i) for |x| ≤ 1

…(ii) for y > 0

Now,

[from(i) & (ii)]

= tan [tan^-1 x + tan^-1 y]

We know that,

for xy < 1

OR

Taking LHS:

Now, we use the formula

for xy < 1

[in the first two terms, we applied the formula]

Now, we again apply the formula, we get

= tan^-1(1)

= RHS

Hence Proved

Find the value of the following:
|x|<1, y<0 and xy < 1.

OR

Prove that: