- ESIC Nursing Officer - 2019 (Shift-2)

ESIC Nursing Officer - 2019 (Shift-2)

Non Nursing Subjects

Easy

Appeared in: ESIC Nursing Officer - 2019 (Shift-2)

Explanation

The problem asks for the value of the expression (1 - tan²45°) / (1 + tan²45°).
The standard value for tan(45°) is 1.
Substituting this value gives (1 - 1²) / (1 + 1²) = (1 - 1) / (1 + 1) = 0 / 2 = 0.
Alternatively, the expression matches the trigonometric identity for cos(2A), which is (1 - tan²A) / (1 + tan²A).
With A = 45°, the expression equals cos(2 * 45°) = cos(90°).
The value of cos(90°) is 0, confirming the result.

Option A: The value of Sin45° is 1/√2 (approximately 0.707), which is not equal to 0.
Option B: The value of tan90° is undefined because it involves division by cos(90°), which is 0.
Option D: The value is 1, not 0. The numerator of the expression evaluates to 0 (1-1), making the entire fraction 0.

Visual 1: Unit Circle Diagram - A diagram of the unit circle highlighting the coordinates at 45° and 90° to show that tan(45°) = y/x = 1 and cos(90°) = x = 0.
Visual 2: Infographic - A graphic illustrating the double angle identity for cosine: cos(2A) = (1 - tan²A) / (1 + tan²A).

Clinical Relevance

Nursing practice connection: Knowing Evaluation of trigonometric expressions using standard angle values and double angle identities helps nurses interpret findings accurately and avoid errors in routine assessment, medication administration, and patient teaching.
This is a non-nursing (mathematics) question.
It tests foundational mathematical skills which are a prerequisite for various competitive examinations.
Proficiency in basic mathematics, including trigonometry, is essential for dosage calculations, understanding biostatistics, and interpreting certain types of medical imaging or data that involve angles and waves.

How to Approach the Question

Step 1: Analyze the given expression: (1 - tan²45°) / (1 + tan²45°).
Step 2: Recall the standard value of the trigonometric function involved. Remember that tan(45°) = 1.
Step 3: Substitute this known value into the expression: (1 - 1²) / (1 + 1²).
Step 4: Simplify the numerator and the denominator. Numerator becomes 1 - 1 = 0. Denominator becomes 1 + 1 = 2.
Step 5: Calculate the final value of the fraction: 0 / 2 = 0.
Step 6: Alternatively, check if the expression matches a known trigonometric identity. Recognize that (1 - tan²A) / (1 + tan²A) is the identity for cos(2A). Apply this with A=45° to get cos(90°), which is 0. Compare the result with the given options to find the correct answer.

Concept Tested & Keywords

Concept Tested: Evaluation of trigonometric expressions using standard angle values and double angle identities.
Stem keywords: trigonometry, tan²45°, expression value
Lead-in keywords: value of

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