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In a right angled triangle ABC, right angled at C,in which AB=13cm,BC=5cm and angle ABC=teta,then the value of cos square teta-sin square teta?
Most Upvoted Answer
In a right angled triangle ABC, right angled at C,in which AB=13cm,BC=...
Solution:
Given:
- AB = 13 cm
- BC = 5 cm
- Angle ABC = θ
To Find:
Cos²θ - Sin²θ
Explanation:
- In a right-angled triangle, the hypotenuse is the longest side and is opposite to the right angle.
- In triangle ABC, AB is the hypotenuse.
- Using Pythagoras theorem, we can find the length of the third side AC:
- AC² = AB² - BC²
- AC² = 169 - 25
- AC² = 144
- AC = 12 cm
- Now, we can find the values of Sinθ and Cosθ:
- Sinθ = BC/AB = 5/13
- Cosθ = AC/AB = 12/13
- Using the identity Cos²θ - Sin²θ = Cos2θ, we can find the value of Cos²θ - Sin²θ:
- Cos²θ - Sin²θ = Cos2θ
- Cos2θ = 2CosθSinθ
- Cos2θ = 2(12/13)(5/13)
- Cos2θ = 120/169
Answer:
Cos²θ - Sin²θ = Cos2θ = 120/169
Community Answer
In a right angled triangle ABC, right angled at C,in which AB=13cm,BC=...
-119/169
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In a right angled triangle ABC, right angled at C,in which AB=13cm,BC=5cm and angle ABC=teta,then the value of cos square teta-sin square teta?
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