Question

How do you solve `cosx=sinx`?

Answer 1

`pi/4 or 45^@`

Explanation:

Property of complementary arcs -->
`cos x = sin (pi/2 - x)`
There for,
`sin x = sin (pi/2 - x)`
a. `x = (pi/2 - x)` --> `2x = pi/2` --> `x = pi/4`
b. `x = pi - (pi/2 - x) = pi/2 + x` (Rejected as non-sense)

Answer: `x = pi/4 or 45^@`
Check.
`x = pi/4` --> `sin x = sqrt2/2` --> `cos x = sqrt2/2` . OK