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Solution


Q.

Assertion (A): The tangent of 45° is 1.
Reason (R): For an angle of 45° in a right triangle, the opposite side equals the adjacent side.
1 Both A and R are true, and R is the correct explanation of A.  
2 Both A and R are true, but R is not the correct explanation of A.  
3 A is true, but R is false.  
4 A is false, but R is true.  

Ans.

(1)

In ΔABC, right angled at B, let ∠C = 45°.⇒ ∠A = 90° – 45° = 45° ⇒ ∠A = ∠C⇒ AB = BC = x (say)[∵ In a triangle, sides opposite to equal angles are equal]∴ tan C = tan 45° = AB / BC …(i) [where AB is perpendicular (opposite side) and BC is base (adjacent side)]⇒ tan 45° = x / x = 1 [∵ AB = BC = x]

Hence, assertion A is true.

Also reason (R) is true and represents a fact (that for an angle of 45° in a right triangle, the opposite side equals the adjacent side), supporting assertion (A), so it correctly explains the assertion (A).