Question

In a right triangle ABC, right angled at B, if tan A = 1, then verify that 2 sin A cos A = 1.

Answer 1

Answer:

In triangle ABC right angled at C

TanA=1

LHS,

2SinACosA

=2sin45cos45

=2×1√2×1√2

=2/√2×√2

=2/2

=1

=RHS

Hence, verified

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Answer 2

Answer:

hey mate here is your answer....

Step-by-step explanation:

▶️ In triangle ABC tan A = BC / AB = 1

▶️ BC = AB

▶️ Let AB = BC= k , where k is a positive number.

▶️ Now, AC = √ AB² + BC²

➡️ √ (k)² + (k)² = k√2

➡️ Therefore, sinA = BC / AC = 1 / √2

➡️ and cosA = AB / AC = 1 / √2

▶️ So 2sinA cos A = 2( 1/√2)(1/√2) = 1

▶️ Required value is 1.

Hope it helps!