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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 ………..
Q) Prove that Ans: Let’s start from LHS LHS = = = We know that sin2A + cos2A = 1 LHS = = =tan A …….. RHS Hence proved!
Prove that: (sin A – 2 sin^3 A)/(2cos^3 A – cos A) = tan A Read More »
Q) If A and B are acute angles such that sin(A-B) = 0 and 2 cos (A+B) -1 = 0, then find angles A and B. Ans:Â Given that sin(A – B) = 0 Since we know that, sin 00 = 0Â Â Â Â Â Â Â A – B = 0 ……….. (i)
Q) Evaluate Ans: Since sin2θ + cos2θ = 1        = = 5 cos2 60 + 4 sec2 30 – tan2 45 = = = =
Q) Prove that: = 1 + sinθ cosθ Ans: Let’s start from LHS LHS = = = = = We know that, a3 – b3 = (a – b) (a2 + b2 + ab) LHS = = (cos2 θ + sin2 θ + sin θ cos θ) = 1 + sinθ cosθ = RHS …………. Hence
Prove that: cos^2 θ/(1 – tan θ) + sin^3 θ/(sin θ – cos θ) = 1 + sin θ cos θ Read More »
Q) Prove that: = 2 cosec θ Ans: LHS = = = = = = = = 2 cosecθ = RHS ……… Hence Proved !
Prove that: sin θ / (1 + cos θ) + (1 + cos θ) / sin θ = 2 cosec θ Read More »
Q) Prove that: x Ans: Let’s start from LHS LHS = x = x =  x = sin θ x cos θ Now, take RHS RHS = = = = sin θ x cos θ Since LHS = RHS Hence proved!
Prove that: (1/cosθ – cos θ) (1/(sin θ) – sin θ) = 1/(tan θ+ cot θ) Read More »
Q) If cos A + cos2 A = 1, then find the value of sin2 A + sin4 A. Ans: cos A + cos2 A = 1 cos A = 1 – cos2 A cos A = sin2 A…………. (i) Now, sin2 A + sin4 A = (sin2 A) + (sin2 A) 2 by substituting
If Cos A + Cos^2 A = 1, then find the value of Sin^2 A + Sin^4 A. Read More »