Question

The value of sec square (-765°)is​

Answer 1

Value of sec²(- 765°) is 2

Given:

sec²(- 765)°

To Find:

Value

Solution:

Adding or subtracting multiple of 360° in a angle does not make any change in value

secx = 1/cox

cos(-x) = cosx

Step 1:

Rewrite -765° as -2 x 360° - 45°

sec² (-765°)

= sec² (- 720° - 45°)

= sec² (- 2 x 360° - 45°)

= sec²(-45°)

Step 2:

Use identity sec x = 1/cos x

sec²(-45°)

=  1/cos²(-45°)

Step 3:

Use cos (-45°) =cos  45°)   value of cos 45° = 1/√2 and simplify

= 1/(1/√2)²

= 2

Value of sec²(- 765°) is 2