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Solution


Q.

Assertion(A):The tangent of 45° is 1.

Reason(R):The cosine of 90° is 0.
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 △ABC, 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).