Question -
Answer -
Given:
Sin x + cos x = 0 and x lies in fourth quadrant.
Sin x┬а= -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 = тИЪ(1 + tan2┬аx)
Cos x = 1/sec x
Sin x = тАУ тИЪ(1- cos2┬аx)
Now,
Sec x = тИЪ(1 + tan2┬аx)
= тИЪ(1 + (-1)2)
= тИЪ2
Cos x = 1/sec x
= 1/тИЪ2
Sin x = тАУ тИЪ(1 тАУ cos2┬аx)
= тАУ тИЪ(1 тАУ (1/тИЪ2)2)
= тАУ тИЪ(1 тАУ (1/2))
= тАУ тИЪ((2-1)/2)
= тАУ тИЪ(1/2)
= -1/тИЪ2
тИ┤ sin x = -1/тИЪ2 and cos x= 1/тИЪ2