Q) Find the value of X if 2 cosec2 300 + X sin2 600 – (3\4) tan2 300 = 10 Ans: Given that,
Find the value of x if 2 cosec2 30 + x sin2 60 – 3/4 tan2 30 = 10 Read More »
trigonometry
Q) If tan (A + B) = √3 and tan (A – B) = ; 0° < A + B < 90°; A > B, find A and B. Ans: Given that, tan (A + B) = √3 = tan 60° Hence, A + B = 60° ………… (i) Next, its given that, tan (A –
If tan (A + B) = √3 and tan (A – B) = 1/(√3) ; 0° < A + B B, find A and B. Read More »
Q) Prove that: Ans: Let’s start from LHS = = = = We know that, a3−b3 formula is = (a−b)(a2 + b2 + ab) = = = = sec θ cosec θ + 1 = 1 + sec θ cosec θ = RHS Hence ProvedÂ
Prove that: tan θ /(1 – cot θ) + cot θ / (1 – tan θ) = 1 + sec θ cosecθ Read More »
Q) Prove that: = 2 cosec Ans: Let’s start from LHS LHS = Since sec A = LHS = = = = = = = = = = = = 2 cosec = RHS …………… Hence ProvedÂ
Prove that root[(sec A – 1)/(sec A + 1)] + root[(sec A + 1)/(sec A – 1)] = 2 cosec A Read More »
Q) If a cos θ + b sin θ = m and a sin θ – b cos θ = n, then prove that a2 + b2 = m2 + n2 Ans: Since a cos θ + b sin θ = m By squaring on both sides, we get: (a cos θ + b sin θ)2
Q) If sin θ – cos θ = 0, then find the value of sin4 θ + cos4 θ. Ans: Since sin θ – cos θ = 0 sin θ = cos θ hence tan θ = 1 and θ = 450 and hence sin 450  = cos 450 = sin4 θ + cos4 θ =
If sin θ – cos θ = 0, then find the value of sin^4 θ + cos^4 θ. Read More »
Q) Evaluate 2sec2 θ + 3 cosec2 θ – 2 sin θ cos θ if θ = 450. Ans: Since θ = 450, sec 450 = √2, cosec 450 = √2, sin 450 = ; cos 450 = 2sec2 θ + 3 cosec2 θ – 2 sin θ cos θ = 2 (√2)2 + 3 (√2)2
Evaluate 2sec^2 θ + 3 cosec^2 θ – 2 sin θ cos θ if θ = 45. Read More »
Q) If θ is an acute angle and sin θ = cos θ, find the value of tan2 θ + cot2 θ – 2. Ans: tan2 θ + cot2 θ – 2. = + – 2 By sin θ = cos θ (given), = + – 2 = 1 + 1 – 2 = 0
If θ is an acute angle and sin θ = cos θ, find the value of tan^2 θ + cot^2 θ – 2. Read More »
Q) Evaluate (5/cot2 30°) + (1/ sin2 60°) – cot2 45° + 2 sin2 90° Ans: Givent that, – cot2 45 + 2 sin2 90 = + – (1)2 + 2 (1)2 = + – 1 + 2 = 3 – 1 + 2 = 4
Evaluate (5/cot^2 30) + (1/ sin^2 60) – cot^2 45 + 2 sin^2 90 Read More »
Q) Prove that sec A (1- sin A)(sec A + tan A) = 1 Ans: Let’s start from LHS LHS = sec A (1- sin A)(sec A + tan A) = = = We know that sin2A + cos2A = 1 or we can say that, 1 – sin2A = cos2A LHS = = 1 ………..