Maths · Trigonometrical identities and trigonometrical functions
If then the triangle is
If \( \operatorname{Sin}^{2} A+\operatorname{Cos}^{2} B+\operatorname{Sin}^{2} C=1, \) then the triangle \( A B C \) is
- A. isosceles
- B. equilateral
- C. right angled
- D. scalene
Step-by-step solution
Given sin²A + cos²B + sin²C = 1. Using cos²B = 1 - sin²B, we get sin²A + sin²C = sin²B. Express sin²C = sin²(A+B) and simplify to obtain 2 cos B sin A sin C = 0. Since sin A, sin C ≠ 0, cos B = 0 ⇒ B = 90°. Thus triangle is right-angled.
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