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What Is The Meaning Of Geometric

In Mathematics, geometry is one of the important branches that deals with figures, angles, dimensions of things and more. In the study of... View Article

What Is Congruent Triangle

Two triangles are congruent if their sides have the same length and angles have the same measure. Consider two triangles, say ABC and PQR,... View Article

What Is Orthocentre

The orthocenter of a triangle is the point where all the three altitudes intersect each other. Orthocenter lie, -inside the triangle for an... View Article

What Is A Singular Matrix

A square matrix is singular if and only if the value of its determinant is zero. Read more. Furthermore, inverse of such matrices does not... View Article

What Is A Median Of A Triangle

A line segment that joins a vertex to the midpoint of the side on its opposite side. Median divides the triangle into 2 smaller triangles having... View Article

What Are Parallel Lines

What are parallel lines? In geometry, parallel lines are the lines which maintain the same distance apart from each other and never intersect at... View Article

What Is Rank Of Matrices

Rank of matrices is the dimension of the vector space obtained by its columns. Rank of a matrix cannot exceed the number of its rows/columns.... View Article

If A C 2b Then Cos C Cos A Sin A Sin C Is Equal To

1) cot B 2) cot 2B 3) tan 2B 4) tan B Answer: (4) tan B Solution: Given, A + C = 2B (cos C - cos A)/(sin A - sin C) = -(cos A - cos... View Article

The Value Of Tan 20 2 Tan 50 Tan 70 Is

1) 1 2) 0 3) tan 50° 4) None of these Answer: (2) 0 Solution: 50° = 70° - 20° Taking “tan” on both sides, tan 50° = tan(70° - 20°) =... View Article

If Sin A Sin B Root3 Cos B Cos A Then Sin 3a Sin 3b Is

1) 0 2) 2 3) 1 4) -1 Answer: (1) 0 Solution: Given, sin A + sin B = √3 (cos B - cos A) Dividing by 2 both sides, 1/2(sin A + sin B) =... View Article

If Cos A B 3 5 And Tan A Tan B 2 Then

1) sin(A + B) = 1/5 2) sin(A + B) = -1/5 3) cos(A - B) = -1/5 4) cos(A + B) = -1/5 Answer: (4) cos(A + B) = -1/5 Solution: Given, cos(A... View Article

If Cos X 3 Cos Y Then 2 Tan Y X 2 Is Equal To

1) cot[(y - x)/2] 2) cot[(x + y)/4] 3) cot[(y - x)/4] 4) cot[(x + y)/2] Answer: (4) cot[(x + y)/2] Solution: Given, cos x = 3 cos y cos... View Article

If Cos Alpha Beta 4 5 And Sin Alpha Beta 5 13 Where 0 Alpha Beta Pi 4 Then Tan 2alpha Is

1) 25/16 2) 56/33 3) 19/12 4) 20/7 Answer: (2) 56/33 Solution: Given, cos(α + β) = 4/5 ⇒ α + β ∈ Ist quadrant sin(α - β) = 5/13 ⇒ α − β... View Article

If Alpha Beta Belongs To 0 Pi 2 Sin Alpha 4 5 And Cos Alpha Beta 12 13 Then Sin Beta

1) 63/65 2) 61/65 3) 3/5 4) 5/13 5) 8/65 Answer: (1) 63/65 Solution: Given, sin α = 4/5 ⇒ cos α = 3/5 And α, β ϵ (0, π/2) ⇒ 0 <... View Article

The Value Of Sin 55 Degree Cos 55 Degree Sin 10 Degree Is

1) 1/√2 2) 2 3) 1 4) √2 Answer: (4) √2 Solution: (sin 55° - cos 55°)/sin 10° = [sin(90° - 35°) - cos 55°]/ sin 10° = (cos 35° - cos... View Article

If Alpha Beta Gamma Belongs To 0 Pi And Are In Ap Then

1) sin β 2) cos β 3) cot β 4) cosec β 5) 2 cos β Answer: (3) cot β Solution: Given that α, β, γ are in AP, then 2β = α + γ. Or β = (α... View Article

If Sin Theta 3 Sin Theta 2 Alpha Then The Value Of Tan Theta Alpha 2 Tan Alpha Is

1) 3 2) 2 3) -1 4) 0 5) 1 Answer: (4) 0 Solution: sin θ = 3 sin (θ + 2α) sin (θ + α - α) = 3 sin (θ + α + α) sin(θ + α) cos α - cos(θ... View Article

If Cos A M Cos B And Cot A B 2 Lambda Tan A B 2 Then Lambda Is

1) m/(m - 1) 2) (m + 1)/m 3) (m + 1)/(m - 1) 4) None of these Answer: (3) (m + 1)/(m - 1) Solution: Given, cos A = m cos B cos A/cos B... View Article

If 0 Less Than Beta Less Than Alpha Less Than Pi 2 Cos Alpha Beta 3 5

1) 0 2) 1 3) 2 4) None of these Answer: (2) 1 Solution: Given, cos(α + β) = 3/5 ⇒ α + β = cos-1(3/5) cos(α - β) = 4/5 ⇒ sin(α - β) =... View Article

If Sin A Cos A Root2 Then The Value Of Cos 2 A Is

1) √2 2) 1/2 3) 4 4) -1 Answer: (2) 1/2 Solution: Given, sin A + cos A = √2 Dividing by √2 on both sides, (sin A + cos A)/√2 = √2/√2... View Article

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