If radii of two concentric circles are 4 cm and 5 cm, then the length of each chord of one circle which is tangent to the other circle is (A) 3 cm (B) 6 cm (C) 9 cm (D) 1 cm The correct answer is (B) 6 cm Solution According to the given data we get to know that OA = 4cm OB = 5cm OA ⊥ BC... View Article
A vertical tower stands on a horizontal plane and is surmounted by a vertical flag staff of height h. At a point on the plane, the angles of elevation of the bottom and the top of the flag staff are α and β, respectively. Prove that the height of the tower is [h tan α/(tan β – tan α)]. Given Avertical flagstaff of height h is surmounted on a vertical tower of height H(say), such that FP = h and FO = H. The angle of... View Article
The shadow of a tower standing on a level plane is found to be 50 m longer when Sun’s elevation is 30° than when it is 60°. Find the height of the tower. Let SQ = h be the tower. ∠SPQ = 30° and ∠SRQ = 60° According to the question, the length of the shadow is 50 m long hen... View Article
The angle of elevation of the top of a tower from two points distant s and t from its foot are complementary. Prove that the height of the tower is √st . Let BC = s; PC = t Let height of the tower be AB = h. ∠ABC = θ and ∠APC = 90° – θ... View Article
Given that sinθ + 2cosθ = 1, then prove that 2sinθ – cosθ = 2. Given sin θ +2 cos θ = 1 To Prove 2sinθ – cosθ = 2 Proof sinθ + 2cosθ = 1 On squaring... View Article
If 1 + sin2θ = 3sinθ cosθ , then prove that tanθ = 1 or 1/2. Given 1+sin2 θ = 3 sin θ cos θ To Prove tanθ = 1 or 1/2 Proof 1+sin2 θ = 3 sin... View Article
The angle of elevation of the top of a tower from certain point is 30°. If the observer moves 20 metres towards the tower, the angle of elevation of the top increases by 15°. Find the height of the tower. Let PR = h meter, be the height of the tower. The observer is standing at point Q such that, the distance between the observer and tower is QR =... View Article
Prove that √(sec2 θ + cosec2 θ) = tan θ + cot θ To Prove √(sec2 θ + cosec2 θ) = tan θ + cot θ Proof Considering LHS √(sec2 θ +... View Article
If cosecθ + cotθ = p, then prove that cosθ = (p2 – 1)/ (p2 + 1). Given cosecθ + cotθ = p To Prove cosθ = (p2 – 1)/ (p2 + 1) Proof cosec θ + cot θ = p (Given)... View Article
Prove the following: tan θ + tan (90° – θ) = sec θ sec (90° – θ) To Prove tan θ + tan (90° – θ) = sec θ sec (90° – θ) Proof On considering L.H.S tan θ + tan... View Article
Prove the following: 1 + (cot2 α/1 + cosec α) = cosec α To Prove 1 + (cot2 α/1+cosec α) = cosec α Proof On considering L.H.S 1 + (cot2 α/1+cosec α) And,... View Article
Prove the following: (√3 + 1) (3 – cot 30°) = tan3 60° – 2 sin 60° To Prove (√3+1) (3 – cot 30°) = tan3 60° – 2 sin 60° Proof On considering L.H.S (√3 + 1) (3 – cot... View Article
Prove the following: (sin α + cos α) (tan α + cot α) = sec α + cosec α To Prove (sin α + cos α) (tan α + cot α) = sec α + cosec α Proof On considering L.H.S (sin α + cos... View Article
Prove the following: If tan A = 3/4, then sinA cosA = 12/25 According to the given details tan A = 3/4 We know that tan A = perpendicular/ base So, tan A = 3k/4k Where, Perpendicular = 3k... View Article
Prove the following: tan A/(1 + secA) – tan A/(1-secA) = 2cosec A To Prove tan A/(1+secA) – tan A/(1-secA) = 2cosec A Proof Let us consider the LHS => On taking the LCM of denominators we obtain =>... View Article
Prove the following: sin θ/(1 + cos θ) + (1 + cos θ)/sin θ = 2cosec θ To Prove sin θ/(1+cos θ) + (1+ cos θ)/sin θ = 2cosec θ Proof Let us consider the LHS On taking the LCM we... View Article
(tan θ + 2) (2 tan θ + 1) = 5 tan θ + sec2 θ. Write ‘True’ or ‘False’ and justify your answer. Answer The given statement is False Solution (tan θ+2) (2 tan θ+1) = 2 tan2 θ + tan θ + 4 tan θ + 2... View Article
If cosA + cos2A = 1, then sin2A + sin2A = 1. Write ‘True’ or ‘False’ and justify your answer. Answer The given statement is True Solution We know that cos A+cos2 A = 1 cos A = 1- cos2 A We get, cos A... View Article
√((1- cos2θ) sec2 θ) = tan θ Write ‘True’ or ‘False’ and justify your answer. Answer The given statement is True Solution We know that Hence the given expression can be expressed as... View Article
The value of the expression (sin 80° – cos 80°) is negative. Write ‘True’ or ‘False’ and justify your answer. Answer The given statement is False Solution sin θ increases when 0° ≤ θ ≤ 90° cos θ decreases when 0°... View Article