Question

answer it fasttttttttttt​

Answer 1

Sec(theta) + cos(theta) = 5/2

Sec(theta) + 1/sec(theta) = 5/2

(sec^2(theta)+1) / sec(theta) = 5/2

2sec^2(theta) + 2 = 5sec(theta)

2sec^2(theta) - 5sec(theta) + 2 = 0

Let sec(theta)=x

then,

2x^2 - 5x + 2 = 0

2x^2 - (4+1)x + 2 = 0

2x^2 - 4x -x + 2 = 0

2x(x-2)-1(x-2)=0

(2x-1)(x-2)=0

Either (2x-1)=0 => x=1/2 => sec(theta)=1/2 [Since sec(theta)=x]

Or (x-2)=0 => x=2 => sec(theta)=2 [Since sec(theta)=x]

Then sec(theta) = 1/2 or 2

Case 1: sec(theta) = 1/2

Now we have Sec(theta) + cos(theta) = 5/2

1/2 + cos(theta) = 5/2

cos(theta) =(5/2 - 1/2)

cos(theta)=2

then,

Sec(theta) - cos(theta) = (1/2 - 2) = -3/2

Case 2: sec(theta) = 2

Now we have Sec(theta) + cos(theta) = 5/2

2 + cos(theta) = 5/2

cos(theta) =(5/2 - 2)

cos(theta)=1/2

then,

Sec(theta) - cos(theta) = (2 - 1/2) = 3/2

therefore

sec(theta) - cos(theta)=3/2 or-3/2