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 […]
trigonometry
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)
Prove that: (1 + cot² θ) (1 – cos θ) (1 + cos θ) = 1 Read More »
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
Prove that (1 + cot^2 A) / (1 + tan^2 A) = cot^2 A Read More »
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)
If sin θ + cos θ = p and sec θ + cosec θ = q, then prove that q (p2 – 1) = 2p Read More »
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
Evaluate: (5 cos 2 60 + 4 sec 2 30 – tan 2 45) / (sin 2 30 + sin 2 60) Read More »
Q) If sin (A – B) = , cos (A + B) = ; 0 < A + B <= 90°, A > B; find ∠ A and ∠ B. Ans: Let’s take the components one by one: Step 1: sin (A – B) = Since we know that sin 300 = ∴ sin (A –
If sin (A – B) = 1/2, cos (A + B) = 1/2; 0 < A + B B; find ∠ A and ∠ B. Read More »
Q) Prove that : Ans: Let’s start with LHS: LHS = = = = = = ∵ sin2 θ + cos2 θ = 1 ∴ LHS = = = = = = = By dividing the numerator & denominator by cos θ, we get: = = = = RHS Hence Proved ! Please press “Heart” button
Prove that : (sin θ – cos θ + 1) / (sin θ + cos θ – 1) = 1/ (sec θ – tan θ) Read More »
Q) Evaluate : 5 tan 60° / (sin2 60° + cos2 60°) tan 30° Ans: We know that: tan 600 = √ 3, sin 60 0 = , cos 600 = ; tan 300 = ; By submitting these values in the given expression, we get: = = = 5 √3 x √3 = 5
Evaluate : 5 tan 60° / (sin2 60° + cos2 60°) tan 30° Read More »
Q) In Δ ABC, if AD ⊥ BC and AD2 = BD x DC, then prove that ∠BAC = 900 Ans: Since AD ⊥ BC, ∴ ∠ ADB = ∠ ADC = 900 By Pythagoras theorem in Δ ADB, we get: AD2 + BD2 = AB2 ……………. (i) Similarly in Δ ADC, by Pythagoras theorem,
In Δ ABC, if AD ⊥ BC and AD2 = BD x DC, then prove that ∠BAC = 90° Read More »