Question

Classwork
If tan x = 1, evaluate Sin x+ cos x, leaving your answer in surd form

Answer 1

sin x + cos x =
`√(2)`

Explanation:

given

tan x = 1 , then

x =
`tan^(-1)` (1) = 45°

the exact values of both sin45° and cos45° =
`(1)/(√(2) )` , then

sin x + cos x

= sin45° + cos45°

=
`(1)/(√(2) )` +
`(1)/(√(2) )`

=
`(2)/(√(2) )`

rationalise the denominator by multiplying numerator/ denominator by
`√(2)`

=
`(2(√(2)) )/(√(2)(√(2)) )`

=
`(2√(2) )/(2)`

=
`√(2)`