trigonometry

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 […]

Q) If 4 cot2 45° – sec2 60° + sin2 60° + p =   then find the value of p. Ans: VIDEO SOLUTION STEP BY STEP SOLUTION 4 cot2 45° – sec2 60° + sin2 60° + p = 4 (1)2 – (2)2  + 4 – 4 + + p = p = 0 Therefore,

Q) Prove that, 2(sin6 θ + cos6 θ) – 3 (sin4 θ + cos4 θ) +1 = 0 Ans: We know that, (a-b)3 = a3 – b3 – 3ab (a – b) And (a-b)2 = a2 + b2 – 2ab LHS: 2(sin6 θ + cos6 θ) – 3 (sin4 θ + cos4 θ) +1 = 2[sin6

Q) If tan θ = , then show that  = Ans: Given that, tan θ =    cot θ = √7 Let’s start from numerator of LHS: cosec2 θ – sec2 θ = (1 + cot2 θ) – (1 + tan2 θ) = cot2 θ – tan2 θ = (√7)2 – = 7 – = …………………

Q) If sin θ + sin2 θ  = 1, then prove that cos2 θ + cos4 θ = 1. Ans:  Given that sin θ + sin2 θ  = 1   sin θ = 1 – sin2 θ LHS:  cos2 θ + cos4 θ = (1- sin2 θ) + (1- sin2 θ)2 = sin θ  + (sin

Q) Prove that (cosec A – sin A) (sec A- cos A) = Ans:  Let’s start with LHS: (cosec A – sin A) (sec A- cos A) =   ( – A) ( – A) =   () () =   () () =   cos A . sin A Now, Let’s solve RHS: =      =      =

Q) Prove that, Ans: 2 methods to solve this question: 1st Method: LHS      =          =        Multiplying numerator & denominator by (sin θ + cos θ + 1), we get: x =       =       We know that sin2 θ + cos2 θ = 1 =                 =      

Q)  If sin α = 1/√2 and cot β = √3, then find the value of cosec α + cosec β. Ans:    VIDEO SOLUTION STEP BY STEP SOLUTION Given that, sin α =  1/√2 ⇒ cosec α = 1 / sin α = 1/ (1/√2) ⇒ cosec α = √2 …………(i) Next, we have value

Q)   If Sin θ + cos θ = √3, then find the value of Sin θ . Cos θ Ans:  Given that Sin θ + cos θ = √3 Let’s square on both sides => (Sin θ + cos θ)2 = (√3) 2 ⇒ Sin2 θ + Cos2 θ +2 Sin θ Cos θ =