In a right triangle ABC, right- angled at B, if tan A = 1, then verify that 2 sin A cos A =1
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13
Answer:
1
Step-by-step explanation:
In ΔABC,
⇒ tan A = (BC/AB) = 1
∴ BC = AB
Let AB = BC = k {K be some constant}
Now,
AC = √AB² + BC²
= √k² + k²
= √2k²
= k√2
Therefore,
(i) SinA = (BC/AC)
= k/k√2
= 1/√2
(ii) CosA = (AB/AC)
= k/k√2
= 1/√2
So,
2 sinA cosA
= 2 (1/√2)(1/√2)
= 2 (1/2)
= 1
Therefore, 2 sinA cosA = 1
Hope it helps!
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Answered by
4
Answer:
- 2 sin A cos A = 1
- 1 = 1
Step-by-step explanation:
Given
- In a right angled Δ ABC, right angled at B,
- tan A = 1
To find
- To verify that 2 sin A cos A = 1.
Solution
In ΔABC, tan A = BC/AB = 1
BC = AB
Let AB = BC = k, where k is a positive number
- AC = √AB² + BC²
- AC = √(k)² + (k)²
- AC = k√2
(Pythagoras theorem)
Therefore,
- sin A = BC/AC = 1/√2
- cos A = AB/AC = 1/√2
Now,
- 2 sin A cos A = 1
- 2(1/√2)(1/√2) = 1
- 1 = 1
- L.H.S = R.H.S
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