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tan 47 °/cot 43 ° = 1 Write ‘True’ or ‘False’ and justify your answer.

Answer The given statement is True Solution tan 47o/cot 43 ° We know that tan (90° -θ) = cot θ \(\begin{array}{l}\frac{\tan 47}{\cot 43}=\frac{\tan... View Article

If cos 9α = sinα and 9α < 90°, then the value of tan5α is (A) 1/√3 (B) √3 (C) 1 (D) 0

The correct answer is (C) 1 Solution cos 9∝ = sin ∝ and 9∝<90° i.e. 9α is an acute angle We know that,... View Article

The value of (tan1° tan2° tan3° … tan89°) is (A) 0 (B) 1 (C) 2 (D) 1/2

The correct answer is (B) 1 Solution According to the given details tan 1°. tan 2°.tan 3° …… tan 89° =... View Article

If cos (α + β) = 0, then sin (α – β) can be reduced to (A) cos β (B) cos 2β (C) sin α (D) sin 2α

The correct answer is (B) cos 2β Solution According to the given details cos(α+β) = 0 Since, cos 90° = 0 We... View Article

Given that sinθ = a/b , then cosθ is equal to (A) b/√(b²– a²) (B) b/a (C) √(b²-a²)/b (D) a/√(b²-a²)

(a) b/√(b2– a2) (b) b/a (c) √(b2– a2)/b (d) a/√(b2– a2) Solution Given that sin θ = a/b We know, sin2 θ +cos2 θ... View Article

The value of the expression [cosec (75° + θ) – sec (15° – θ) – tan (55° + θ) + cot (35° – θ)] is (A) – 1 (B) 0 (C) 1 (D) 3 2

The correct answer is (B) 0 Solution As per the given details We have to determine the value of the equation,... View Article

If sin A = 1/2 , then the value of cot A is (A) √3 (B) 1/√3 (C) √3/2 (D) 1

The correct answer is (A) √3 Solution As per the given details Sin A = ½ … (i) We know... View Article

If cos A = 4/5, then the value of tan A is (A) 3/5 (B) 3/4 (C) 4/3 (D) 5/3

The correct answer is (B) 3/4 Solution As per the given details cos A = 4/5 …(i) We know, tan... View Article

The points A (x1, y1), B (x2, y2) and C (x3 y3) are the vertices of ABC. (i) The median from A meets BC at D. Find the coordinates of the point D. (ii) Find the coordinates of the point P on AD such that AP : PD = 2 : 1 (iii) Find the coordinates of points Q and R on medians BE and CF, respectively such that BQ : QE = 2 : 1 and CR : RF = 2 : 1 (iv) What are the coordinates of the centroid of the triangle ABC?

As per the given details The vertices of ΔABC = A, B and C Coordinates of A, B and C... View Article

A (6, 1), B (8, 2) and C (9, 4) are three vertices of a parallelogram ABCD. If E is the midpoint of DC, find the area of △ ADE.

Given The three vertices of a parallelogram ABCD are A (6, 1), B (8, 2) and C (9, 4) Find... View Article

If (- 4, 3) and (4, 3) are two vertices of an equilateral triangle, find the coordinates of the third vertex, given that the origin lies in the interior of the triangle.

Given Two vertices of an equilateral triangle= (– 4, 3) and (4, 3) Find out We have to determine the third... View Article

In what ratio does the x-axis divide the line segment joining the points (- 4, – 6) and (-1, 7)? Find the coordinates of the point of division.

Let the ratio in which x-axis divides the line segment joining (–4, –6) and (–1, 7) = 1: k. Then... View Article

Find the area of the triangle whose vertices are (-8, 4), (-6, 6) and (-3, 9).

Given The vertices are: (x₁, y₁) = (-8, 4) (x₂, y₂) = (-6, 6) (x₃, y₃) = (-3, 9) Find... View Article

If the point A (2, – 4) is equidistant from P (3, 8) and Q (-10, y), find the values of y. Also find distance PQ.

The given points are A (2, – 4) P (3, 8) and Q (–10, y). We have to determine the... View Article

Find the value of m if the points (5, 1), (-2, -3) and (8, 2m) are collinear.

Given We are given with the points (5, 1), (–2, –3) and (8, 2m) that are collinear Find out We... View Article

Find the coordinates of the point Q on the x-axis which lies on the perpendicular bisector of the line segment joining the points A (-5, -2) and B(4, -2). Name the type of triangle formed by the points Q, A and B.

Point Q is the midpoint of AB as the point P lies on the perpendicular bisector of AB. From mid point... View Article

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