sin(90+A)-cosA is equal to?
Answers
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
