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प्रश्न
If 0 ≤ x ≤ 90°, state the numerical value of x for which sin x° = cos x°.
संख्यात्मक
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उत्तर
Given: sin x° = cos x°, where 0° ≤ x ≤ 90°.
Step-wise calculation:
1. Check endpoint x = 90°:
cos 90° = 0 while sin 90° = 1
So, x = 90° is not a solution.
2. For 0° ≤ x < 90° we may divide both sides by cos x (cos x ≠ 0): tan x = 1.
3. Solve tan x = 1
⇒ x = arctan(1)
= 45°
Equivalently, sin x = cos x implies sin x = sin (90° – x).
So, x = 90° – x
⇒ 2x = 90°
⇒ x = 45°
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