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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 »
Q) Prove that : (cosec θ – sin θ) (sec θ – cos θ) (tan θ + cot θ) = 1 Ans: Let’s start with LHS: LHS: (cosec θ – sin θ) (sec θ – cos θ) (tan θ + cot θ) = = = = = = 1 Please do press “Heart” button if you
Prove that : (cosec θ – sin θ) (sec θ – cos θ) (tan θ + cot θ) = 1 Read More »
Q) Evaluate : (sec2 450 – tan2 450)/sin2 450 Ans: We know that: sec 450 = , tan 450 = 1, sin 450 = ; By submitting these values in the given expression, we get: = = = 1 x 2 = 2 Hence the value of the given function is 2. Please do press “Heart”
Q) Prove that Ans: Let’s start solving from LHS: = = = = = ∵ sin2 A + cos2 A = 1, ∴ cos2 A = 1 – sin2 A ∴ LHS = = = = RHS…. Hence Proved ! Please press the “Heart”, if you like the solution.
Q) Evaluate: (2𝑠𝑖𝑛 2 600 − 𝑡𝑎𝑛 2 300) / 𝑠𝑒𝑐2 450 Ans: We know that: sin 600 = ; tan 300 = ; sec 450 = By submitting these values in the given expression, we get: = = = = = Please do press “Heart” button if you liked the solution.
Q) If cosθ + sin θ = 1 , then prove that cosθ – sinθ = ±1 Ans: VIDEO SOLUTION STEL BY STEP SOLUTION Given that If cosθ + sinθ = 1 Step 1: We square the above equation on both sides, we get: (cos θ + sin θ) = (1) ∴ cos2 θ + sin2
If cosθ + sinθ = 1 , then prove that cosθ – sinθ = ±1 Read More »
Q) Evaluate : (cos 450 + sin 600) / (sec 300+ cosec 300). Ans: We know that: cos 450 = ; sin 600 = ; sec 300 = ; cosec 300 = 2 By submitting these values in the given expression, we get: (cos 450 + sin 600) / (sec 300+ cosec 300) = =
Evaluate : (cos 45° + sin 60°) / (sec 30° + cosec 30°). Read More »
Q) Prove that Ans: Let’s start from LHS: LHS = = We know that sin2 θ + cos2 θ = 1 By substituting this value in the above equation, we get: LHS = = = = = = = Hence Proved ! Please do press “Heart” button if you liked the solution.
Prove that (sin θ – 2 sin3 θ) / (2 cos3 θ – cos θ) = tan θ Read More »
Q) Prove that , if . Ans: Let’s start from LHS: LHS = = = = = = ∵ . ∴ and ∴ LHS = = = = = = RHS Hence Proved ! Please do press “Heart” button if you liked the solution.
Prove that (cosec 2 θ – sec 2 θ) / (cosec 2 θ + sec 2 θ) = 3/4, if tan θ = 1/√7. Read More »
Q) prove that sin 6 θ + cos 6 θ = 1 – 3 sin 2 θ cos 2 θ Ans: Let’s start from LHS LHS = prove that sin 6 θ + cos 6 θ = (sin 2 θ) 3 + (cos 2 θ) 3 We know that a 3 + b 3 = (a + b) (a
prove that sin 6 θ + cos 6 θ = 1 – 3 sin 2 θ cos 2 θ Read More »