trigonometry

  Q)  Prove that : tan θ /(1 – cot θ) + cot θ / (1 – tan θ) = 1 + sec θ + cosec θ Ans:  Here, let’s start by simplifying the LHS in given equation: LHS = = = = = = Now, we know that a3 – b3 = (a – b) (a2 […]

  Q)  If sin A = and cos B = , then find the value of (tan A + tan B) Ans: We To find the value of tan A + tan B, we need to find the value of tan A and tan B Step 1: We are given sin A = We know

  Q)  If tan θ + sec θ = m, then prove that sec θ = . Ans: We are given: tan θ + sec θ = m ………… (i) Next, we calculate value of tan θ + sec θ To do that, we multiply and divide (tan θ + sec θ) by (tan θ

  Q)  Prove that : tan θ /(1 – cot θ) + cot θ / (1 – tan θ) = 1 + tan θ + cot θ Ans:  Here, let’s start by simplifying the LHS in given equation: LHS = = = Let’s make the denominators equal: LHS = = = We know that a3

  Q)  Ans:  Here, – – – Please do press “Heart” button if you liked the solution. 

Q) If , then find the value of  , where α is in IV quadrant. Ans:   Since, We know that Now since, α is in IV quadrant, therefore value of will be negative only. Now, Therefore Please do press “Heart” button if you liked the solution. 

Q) If cot θ = then evaluate that Ans:   Please do press “Heart” button if you liked the solution. 

Q) IF sec θ=(x + 1/4x) then prove that sec θ + tan θ = 2x or 1/2x Ans:   Given When When Therefore, value of Please do press “Heart” button if you liked the solution. 

Q) If sec θ + tan θ = p, obtain the values of sec θ, tan θ and sin θ in terms of p. Ans:   sec θ + tan θ = p ………….. (i) ∵ sec2 θ  – tan2 θ = 1 ∴ (sec θ + tan θ) (sec θ – tan θ) = 1 ∴ p (sec θ – tan θ)

Q) If sin θ = , prove that . Ans:  Let’s start LHS: =  =  ∵ 1- cos2 θ= sin2 θ ∴ LHS =  =  =  =  = cot θ ∵ sin θ =     ∴ cot θ = ∴ LHS = = RHS Hence Proved !