Question

⇔In a right angle triangle abc right angled at b if tan a = 1 , verify that ,
2sin a cos a = 1
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Answer 1

→Question: In a right angle triangle ABC right angled at B if tan a = 1 , verify that ,  2 sin A cos A =1

→Solution:

• In ΔABC tan A = BC ÷ AB = 1
• ∴ BC = AB     ( Cross Multiplication)
• Now, let AB = BC = k , where k is a positive number.
• Now, AC = √AB²+BC²
• √k²+k² = k√2
• ∴ Sin A = BC÷AC = 1÷√2
• ∴ Cos A = AB÷AC = 1÷√2
• ∴ 2 sinA cosA = 2(1÷√2)×(1÷√2) = 1