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If 4 cos A cos B + sin 2A + sin 2B +sin 2C = 4 , then ΔABC is
- a)right angled
- b)isosceles
- c)right angled isosceles
- d)None of these
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
If 4 cos A cos B + sin 2A + sin 2B +sin 2C = 4 , then ΔABC isa)r...
∵ 4cosAcosB+ 4sinAsinBsinC= 4
⇒cos(A − B)≥ 1
⇒cos(A − B)= 1
True if A=B ...(2)
Put (2) in (1)
sinC= 1
C= 90°
⇒cos(A − B)≥ 1
⇒cos(A − B)= 1
True if A=B ...(2)
Put (2) in (1)
sinC= 1
C= 90°
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Community Answer
If 4 cos A cos B + sin 2A + sin 2B +sin 2C = 4 , then ΔABC isa)r...
Given Equation:
4 cos A cos B + sin 2A + sin 2B + sin 2C = 4
Explanation:
To find the type of triangle ΔABC, let's simplify the given equation.
Step 1: Use the trigonometric identities:
sin 2A = 2 sin A cos A
sin 2B = 2 sin B cos B
Step 2: Substitute the identities into the given equation:
4 cos A cos B + 2 sin A cos A + 2 sin B cos B + sin 2C = 4
4 cos A cos B + 2 sin A cos A + 2 sin B cos B + 2 sin C cos C = 4
Step 3: Rewrite the equation:
2(cos A cos B + sin A cos A + sin B cos B + sin C cos C) = 4
2(cos A cos B + sin(A+B) + sin C cos C) = 4
2(cos A cos B + sin C cos C) = 4
cos A cos B + sin C cos C = 2
Step 4: Since cos A cos B + sin C cos C = 2, the triangle ΔABC is a right-angled isosceles triangle.
Therefore, the correct answer is option C - right-angled isosceles triangle.
4 cos A cos B + sin 2A + sin 2B + sin 2C = 4
Explanation:
To find the type of triangle ΔABC, let's simplify the given equation.
Step 1: Use the trigonometric identities:
sin 2A = 2 sin A cos A
sin 2B = 2 sin B cos B
Step 2: Substitute the identities into the given equation:
4 cos A cos B + 2 sin A cos A + 2 sin B cos B + sin 2C = 4
4 cos A cos B + 2 sin A cos A + 2 sin B cos B + 2 sin C cos C = 4
Step 3: Rewrite the equation:
2(cos A cos B + sin A cos A + sin B cos B + sin C cos C) = 4
2(cos A cos B + sin(A+B) + sin C cos C) = 4
2(cos A cos B + sin C cos C) = 4
cos A cos B + sin C cos C = 2
Step 4: Since cos A cos B + sin C cos C = 2, the triangle ΔABC is a right-angled isosceles triangle.
Therefore, the correct answer is option C - right-angled isosceles triangle.
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If 4 cos A cos B + sin 2A + sin 2B +sin 2C = 4 , then ΔABC isa)right angledb)isoscelesc)right angled isoscelesd)None of theseCorrect answer is option 'C'. Can you explain this answer?
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