If \(A + B = 90^\) and \(sin A = 3/5\) , then find the value of \(tan B\) .

Question

If \(A + B = 90^\) and \(sin A = 3/5\) , then find the value of \(tan B\) .

1. A. \(4/3\) (Correct answer)
2. B. \(3/4\)
3. C. \(5/3\)
4. D. \(3/5\)

Correct Answer

Option A — \(4/3\)

Detailed Solution & Explanation

The correct answer is 4/3.

Key Points

• Since A + B = 90°, the angles are complementary, so B = 90° − A and tan B = tan(90° − A) = cot A.
• From sin A = 3/5, the triangle is the 3-4-5 right triangle, giving cos A = 4/5.
• Therefore cot A = cos A / sin A = (4/5) ÷ (3/5) = 4/3.

Additional Information

• The 3-4-5 triple is the most frequently used in trigonometry questions; recognising sin = 3/5 immediately supplies cos = 4/5 and tan = 3/4 without using the Pythagorean identity.
• Other triples worth knowing: 5-12-13, 8-15-17 and 7-24-25.
• Note the reciprocal relationship being tested: tan A = 3/4 while tan B = 4/3, so tan A × tan B = 1 whenever A + B = 90° — a result often asked in its own right.

प्रश्न (हिन्दी में)

यदि \(A + B = 90^\) और \(sin A = 3/5\) हो, तो \(tan B\) का मान ज्ञात कीजिए।

1. A. \(4/3\)
2. B. \(3/4\)
3. C. \(5/3\)
4. D. \(3/5\)