Question -
Answer -
Given:
Sin x + cos x = 0 and x lies in fourth quadrant.
Sin x = -cos x
Sin x/cos x = -1
So, tan x = -1 (since, tan x = sin x/cos x)
We know that, in fourth quadrant, cos x and sec x arepositive and all other ratios are negative.
By using the formulas,
Sec x = √(1 + tan2 x)
Cos x = 1/sec x
Sin x = – √(1- cos2 x)
Now,
Sec x = √(1 + tan2 x)
= √(1 + (-1)2)
= √2
Cos x = 1/sec x
= 1/√2
Sin x = – √(1 – cos2 x)
= – √(1 – (1/√2)2)
= – √(1 – (1/2))
= – √((2-1)/2)
= – √(1/2)
= -1/√2
∴ sin x = -1/√2 and cos x= 1/√2