Q) Evaluate: 2 sin2 300 sec 600 + tan2 600 Ans: We need to find the value of: 2 sin2 300 sec 600 + tan2 600 We know that sin 300 = , sec 600 = 2, tan 600 = √3 by substituting these values in the given expression, we get: 2 sin2 300 sec 600 + tan2 600 = 2 ( […]
trigonometry
 Q) Prove that : Ans: Let’s start from simplifying the LHS: LHS = = = Since, we need to get demnominator in simplified form, hence let’s multiply nominator and denominator by cos θ + sin θ – 1, we get: LHS = = = = = = We know that sin2 θ + cos2
Prove that : 1 + sec θ – tan θ / 1 + sec θ + tan θ = 1 – sin θ / cos θ Read More »
Q) Evaluate: Ans: We need to find the value of: We know that cos 45 = , sec 30 = , cosec 30 = 2 by substituting these values in the given expression, we get: = = = = …. Answer or to further simplify, we can multiply and divide the expression by (√3 –
Q) Prove that Ans: Method 1: We need to prove that Let’s start with squaring in both sides: We know that:  and ∴ ∴ Since LHS = RHS Hence Proved ! Method 2: Let’s start from LHS: Since, and ∴ LHS = = = Since, ∴ LHS = = =   = = =
Prove that Root ( sec^2 θ + csc^2 θ) = tan θ + cot θ Read More »
Q) If x sin3 θ + y cos3 θ = sin θ cos θ and x sin θ = y cos θ, prove that x2 + y2 = 1 Ans: Given that x sin3 θ + y cos3 θ = sin θ cos θ ∴ x sin θ sin2 θ + y cos θ cos2 θ = sin θ
 Q) Evaluate: 2√2 cos 45° sin 30° + 2√3 cos 30° Ans: Here, let’s start values of sin & cosine for θ = 300 and 450 We know that sin 300 = , cos 300 = , cos 450 = We submit these values in the given question, we get: 2√2 cos 45° sin
Evaluate: 2√2 cos 45° sin 30° + 2√3 cos 30° Read More »
 Q) If A = 60° and B = 30°, verify that : sin (A + B) = sin A cos B + cos A sin B Ans: Here, let’s calculate the values of LHS & RHS one by one and check if it is verified. LHS = sin (A + B) = sin (60
If A = 60° and B = 30°, verify that : sin (A + B) = sin A cos B + cos A sin B Read More »
 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
Prove that : tan θ /(1 – cot θ) + cot θ / (1 – tan θ) = 1 + sec θ cosec θ Read More »
 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
If sin A = 3/5 and cos B = 12/13 , then find the value of (tan A + tan B) Read More »
 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
If tan θ + sec θ = m, then prove that sec θ = (m2 + 1)/2m Read More »