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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 – = ………………… […]
trigonometry
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
If sin θ + sin^2 θ = 1, then prove that cos^2 θ + cos^4 θ = 1. Read More »
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: =   =   =
Prove that (cosecA – sinA) (secA-cosA) = 1/(cotA+tanA) Read More »
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 =           =     Â
Prove that, (tanθ + secθ-1)/(tanθ – secθ + 1) = (1 + sinθ)/cosθ Read More »
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
If Sin α = 1/√2 and Cot β = √3, then find the value of Cosec α + Cosec β. Read More »
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 =
If Sin θ + Cos θ = √3, then find the value of Sin θ . Cos θ Read More »