Question

Find the value of the trigonometric equation given by ${\text{cos10}}^\circ {\text{ - sin10}}^\circ$.
${\text{A}}{\text{. Positive}} \\\ {\text{B}}{\text{. Negative}} \\\ {\text{C}}{\text{. 0}} \\\ {\text{D}}{\text{. 1}} \\\$

Answer 1

Hint: To find the value, it is difficult to find the value of angle 10° of cos and sin functions so we find the answer in generic terms by looking at sin and cos functions from angles 0 to 90°.

Complete step-by-step answer:
For the angles 0° to 90°,
Sin function increases its value i.e. starts at sin0°=0 and ends at sin90°=1 and at sin45° it is$\dfrac{1}{{\sqrt 2 }}$.
Cos function value decreases over this interval i.e. starts at cos0°=1 and ends at cos90°=0 and at cos45° it becomes$\dfrac{1}{{\sqrt 2 }}$.
I.e. for angle θ, where 0° ≤ θ ≤ 45°
Cos function value is always greater than sin function value.
⟹${\text{cos10}}^\circ {\text{ - sin10}}^\circ$> 0 = positive.
Hence Option A is the correct answer.

Note: In order to solve this type of questions the key is to identify that cos10° is slightly less than the value of cos0°, i.e. slightly less than 1, whereas sin10° is slightly greater than the value of sin0°, i.e. slightly greater than 0. Hence their difference is always positive as the value of cos function is greater. Adequate knowledge of trigonometric tables of sine and cosine functions is appreciated.