The correct option is .
Further explanation:
Given:
It is given that if .
Step by step explanation:
Step 1:
Complementary angles are those two angles whose sum is equal to .
The given angles are .
Now find the sum of the given angles to check whether these angle are complementary or not.
It can be seen that the sum of the angles is .
Therefore, are complementary angles.
Step 2:
We know that the sine of any acute angle is equal to the cosine of its complement angle.
Therefore, as are complementary angles.
Now consider all the options.
Option A: No, because angles measuring are supplements.
The supplementary angles are those two angles whose sum is equal to .
As it has been proved that are complementary angles.
Thus, option A is not correct.
Option B: No, because angles measuring are complements.
It has been proved that as are complementary angles.
Thus, option B is not correct.
Option C: Yes, because angles measuring are supplements.
This option is also not correct.
Option D: Yes, because angles measuring are complements.
It has been proved that as are complementary angles.
Thus, option D is correct.
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Answer details:
Grade: Middle school
Subject: Mathematics
Chapter: Trignometry
Keywords: sine function, cosine function, complementary angles, supplementary angles, measurement, angles, acute angle, complement, sum of the angles, supplements.