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Assertion (A): tan(90° − θ) = cot θ. Reason (R): In a right triangle the two acute angles are complementary, so the opposite side of one is the adjacent side of the other. Which is correct?

Class 10Introduction to TrigonometryTrigonometry
  • ABoth A and R are true and R is the correct explanation of A
  • BBoth A and R are true but R is not the correct explanation of A
  • CA is true but R is false
  • DA is false but R is true

Step-by-Step Solution

The two acute angles sum to 90°, so the side opposite to θ is adjacent to (90° − θ). This swaps opposite/adjacent, turning tan into cot. R correctly explains A.
Answer: A) Both A and R are true and R is the correct explanation of A

Key idea: Complementary angle identities

Since the two acute angles of a right triangle sum to 90° (complementary), the side that is 'opposite' to one angle is 'adjacent' to the other. This swaps sine and cosine:

**sin(90° − θ) = cos θ**
**cos(90° − θ) = sin θ**
**tan(90° − θ) = cot θ**
**cot(90° − θ) = tan θ**
**sec(90° − θ) = csc θ**
**csc(90° − θ) = sec θ**

**Use**: simplify expressions like sin 70° = cos 20°, cos 80° = sin 10°. Also useful in proof-style questions: 'Show sin 25° / cos 65° = 1.'

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