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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... 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... 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 =... 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 θ cos... 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,... 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 + cosec2 θ) We know that... 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... 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... 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) \(\begin{array}{l}\cot ^{2} \alpha... 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)... 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... 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... 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 =>\(\begin{array}{l}\frac{\tan A}{1+\sec A }... 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 \(\begin{array}{l}\frac{\sin... 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... 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 \(\begin{array}{l}\sin ^{2}\Theta +\cos... View Article

√((1- cos²θ) sec² θ) = tan θ Write ‘True’ or ‘False’ and justify your answer.

Answer The given statement is True Solution \(\begin{array}{l}\sqrt{((1-\cos ^{2}\Theta )\sec ^{2}\Theta }\end{array} \) We know that \(\begin{array}{l}\sin ^{2}\Theta +\cos ^{2}\Theta =1\end{array}... 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... View Article

The value of the expression (cos223° – sin267°) is positive. Write ‘True’ or ‘False’ and justify your answer.

Answer The given statement is False Solution cos2 23° – sin2 67° The given expression can be expressed using the identity (a2-b2) = (a+b)(a-b)... View Article

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