trigonometry

           Q) If sin A = , find the values of cos A and tan A Ans: [Approach: We can calculate the value of cos A by trigonometric identity of sin2 A + cos2 A = 1, and then calculate tan A = sin A / cos A] Step 1: Since we […]

Q). Prove that: sin θ/(cot θ + cosec θ) = 2 + sin θ /(cot θ – cosec θ) Ans. Let’s start from LHS: Step 1: LHS = = = = Step 2: We know that sin2 θ + cos2 θ = 1 ∴ sin2 θ = 1 – cos2 θ ∴ LHS = Step

  Q)  If a cos A + b sin A = m and a sin A – b cos A= n, then a² + b² = ? Ans:  Step 1: Let’s start with 1st equation: a cos A + b sin A = m By squaring both the sides of the equation, we get: (a

  Q)  If in a triangle ABC right angled at B, AB = 6 units and BC = 8 units, then find the value of sin A cos C + cos A sin C. Ans:  Step 1: Let’s make a diagram to better understand the question: Here Δ ABC is a right angle triangle and

  Q)  Prove that: (1 + cot 2 θ) (1 – cos θ) (1 + cos θ) = 1 Ans:  Method 1: Step 1: Let’s start with LHS and put values of cot θ: LHS = (1 + cot 2 θ) (1 – cos θ) (1 + cos θ) = (1 + (  [∵ (a – b)

  Q)  Prove that Ans:  Method 1: Step 1: Let’s start with LHS and put values of cot A and tan A: LHS = = = Step 2: We know that sin 2  A + cos 2  A = 1 = = = Hence Proved ! Method 2: Let’s start with LHS and applying trigonometric

  Q)  Prove that 1 + tan 2 A = sec 2 A Ans:  Step 1: Let’s draw a right angled triangle: Here ABC is a triangle where ∠ B is right angle. Step 2: By applying Pythagoras theorem, we know: AB 2  + BC 2  = AC 2 Step 3: Let’s divide the above

Q) If sin θ + cos θ = p and sec θ + cosec θ = q, then prove that q (p2  – 1) = 2 p. Ans: Let’s take the components one by one: Step 1: Given that sin θ + cos θ = p ∴ p = sin θ  + cos θ ….. (i)

Q) Evaluate: Ans: Let’s take the components one by one: Step 1: we know that cos 60 = , sec 30 = , tan 45 = 1, sin 30 = , sin 60 = Step 2: Let’s put these values in the given expression, we get: ∴ ∴ ∴ ∴ ∴ ∴ Therefore the value of