Question

Prove that `(sinx)^(sqrt(2)) =tan x`?

Answer 1

The statement is false.

Explanation:

We seek to prove that:

`(sinx)^(sqrt(2)) =tan x`

However, We can readily disprove that this identity using a counterexample:

Consider the case `x=pi/4`

Then,:

`LHS = (sin (pi/4))^(sqrt(2))`
`\ \ \ \ \ \ \ \ = ((sqrt2)/2)^(sqrt(2))`
`\ \ \ \ \ \ \ \ ~~ 0.6125`

However,

`RHS = tan(pi/4)`
`\ \ \ \ \ \ \ \ = 1`

As we have identified that there is a specific case `(x=pi/4)` for which the statement is false, then the statement cannot, in general, be true.