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
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... View Article
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... 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... 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 =1 cos2 θ = 1-sin2 θ cos... 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, cosec(75°+θ) – sec(15°-θ) –... 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 that, To determine the... 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 A = sinA/cosA To find the value... View Article
