Question

The value of (sec 45° – cos 45°) is equal to the value of:

Options

• sin 45°

• sin 90°

• cos 90°

• tan 45°

Answer 1

sin 45°

Explanation:

Given expression:

sec 45° – cos 45°

Values of trigonometric ratios:

`sec 45^circ = sqrt(2)`

`cos 45^circ = 1/sqrt(2)`

Calculation:

= `sqrt(2) - 1/sqrt(2)` 

= `((sqrt(2) xx sqrt(2)) - 1)/sqrt(2)`

= `(2 - 1)/sqrt(2)`

= `1/sqrt(2)`

Comparing with options:

(A) `sin 45^circ = 1/sqrt(2)`

(B) sin 90° = 1

(C) cos 90° = 0

(D) tan 45° = 1

Since the calculated value is `1/sqrt(2)`, it matches with sin 45°.