Question

sin(90+A)-cosA is equal to?​

Answer 1

Answer :

sin(90° + A) - cosA

We know that sin(90° - θ) = cosθ

Because 90° is an odd multiple of 90 so the trigonometric ratio will change into cosθ and in quadrant 1 all the trigonometric ratios are positive

So,

sin(90° - θ) = cosθ

Now come to the question

sin(90° - θ) - cosθ

= cosθ - cosθ

= 0

Explanation of the topic:

In the above picture shows about Quadrant angles

Quadrant angles:

If the terminal side of an angle in in standard position coincides with the coordinate axis then the angle is called quadrant angle . 0°,90°,180°,270°,360° are quadrant angles

Quadrant 1 (Q1)

In the first quadrant all trigonometric ratios are positive, that means the trigonometric ratios angle's between 0° to 90° will be positive (0°<θ<90°)

Quadrant 2 (Q2)

In the second quadrant only sinθ & it's reciprocal is positive, that means sinθ & cosecθ are positive (90°<θ<180°)

Quadrant 3 (Q3)

In the third quadrant tanθ & cotθ are positive . When θ lies between 180° to 270° (180°<θ<270°)

Quadrant 4 (Q4)

In the fourth quadrant cos & sec are positive. When θ lies between 270° to 360° (270°<θ<360°)

Note:

See the 2nd picture you will understand by using 3rd step in the answer