If cosA= 1/√17 and cosB = 3/√34, then show that: A+B = 3π/4.   Answer : Since, we have been asked to prove the value of A+B = 3π/4 and we know it well that, π=180° So, 3π/180 = 135°. We now have to use the formula of cos(A+B) or sin(A+B) because we need to prove the given value of A+B. For this, we first find out sinA and sinB becau…

Find the value of: cot22°.cot23° -cot22° -cot23° = 1  Answer: As we had been discussing continuously in our latest posts, if you have the questions where the given angles are unknown to you. You don't know the Trigonometric values of those angles without using calculator then, you need to either sin or difference the given angle…

tan29° +tan16° +tan29°.tan16° = 1 Answer: For all the questions, where you have angles whose values are not known to you. You will do very easy step! You either find the sum or difference of the given angles and try to get the angle whose value is known to you! Here, in this case, we have 29° and 16°. Now, if we add these angles, ou…

Prove that: 1- tan35°.tan10° = tan35° + tan10°  Answer: So, when you glare the question once, you and send the LHS to divide the RHS by taking 1 common on the LHS, then you will observe that you get the formula of tan(A+B) on the right side. But, now it's about what are the angles and is it a sum formula or difference formula of…

Prove that: (cos40° -sin40°)/(cos40°+sin40°) = tan5°  Answer: You need to remember that if the questions have no any angle whose value is known to you then, you need to use the sum or difference formula according to the given condition. Here, we have 40° in the left and 5° in the right! What if we find difference of both angles? We …

Prove that: (cos20°- sin20°)/(cos20° +sin20°} = tan25°  Answer: We already have been discussing about compound angles in previous blog posts.  And I think it's fair not to explain everything in detail. Rather, let's know that tan(45°-A) = (1+tanA)/(1-tanA) We know, Tan(A-B)= $\dfrac{tanA-tanB}{1+tanA.tanB}$ When you replace …

Prove that: tan²A -tan²B = {sin(A+B).sin(A-B)}/ cos²A.cos²B   Answer: Okay, so this question is kind of irritating one because it has so much repeated processes in the solution. But don't worry. We are here to help you. First of all, you need to know the formula of Compound Angles to start the solution as given sin(a+b) and sin(…

Prove that: (tan4A-tan3A)/(1+ tan4A.tan3A) = tanA  Answer: This question might seem difficult at the first glance. So, what I suggest is: 'Take the problem easily but seriously.' Therefore, look for the possibilities. When I looked, I knew the formula of tan2A and tanA but I had not read the use of tan4A nor tan3A. Then, I l…

Prove that: sin(45°+A) -cos(45°-A) = 0  Amswer: To solve such questions, you must have the knowledge about Trigonometric Ratios of Compound Angles as you will need them to open the starting of the solution. Similarly, you will also require the basic knowledge of algebraic expressions cause whatever you will solve here is based on al…

Prove that: 1- 2sin²(45°-α) = 2sinα.cosα  Answer: This question is also very easy to solve if you know the two basic things: one is the formula of Trigonometric Ratios of Compound Angles and the other is how to solve algebraic expressions. On a side note, the value of RHS i.e. 2 sinA.cosA = sin2A, so, if any way you can get the LHS…

Prove that: 2cos(45°+Θ).cos(45°-Θ) = cos²Θ- sin²Θ  Answer: You have two ways of bringing the conclusion. One is the way I solved this question and the other is to get cos2Θ as we know cos²Θ-sin²Θ = cos2Θ. But, solving it the way I solved, we need to first know the formula of Trigonometric Ratios of Compound Angles. You can see the f…

Prove that:  2sin(45°+Θ).sin(45°-Θ) = cos^2 Θ -sin^2  Θ Answer: This question is similar to the one we just posted previously. You need to know the formulas for expanding the compound angles and then you can easily solve such questions in Trigonometry of Mathematics. #SciPiTutor #CompoundAngles #Trigonometry #Mathematics

Prove that:  sin(45°+A).sin(45°-A) =1/2(cos^2A-sin^2A) Answer: So, to solve this question you will need to understand the Trigonometric Ratios of Compound angle's formulas. See the formulas below and you will be able to solve the questions related to this! #SciPiTutor #CompoundAngles #Trigonometry #Mathematics

Prove that: sin5Θ -sin3Θ +sin2Θ = 4sinΘ.cos3Θ/2.cos5Θ/2   Answer: So, to solve this type of questions you need to understand the given formula of Trigonometry. Here, it's not exactly compound angles but yeah, you can term them as compound angles. Also, sin2A = 2 sinA.cosA Therefore, with all the above mentioned formula in mind, …

Find the value of sin(13π/12). Answer: Advertisement The first thing you need to keep in your mind is that value of π(Pi) is equal to 180°. And then you need to know the CAST FORMULA and finally you need to know the given formulas of Compound Angles. #SciPiTutor #CompoundAngles #Trigonometry #Mathematics

Prove that: Sin(45°+A) + cos(45°+A) =√2 cosA Answer: You need to understand the given formulas to be able to solve such types of Trigonometric values of compound angles questions and answers. Solution: Taking LHS = sin(45°+A) +cos(45°+A) = sin45°.cosA +cos45°.sinA + cos45°.cosA -sin45°.sinA = $\frac{1}{√2}$.cosA + $\frac{1}{√2}$.sin…

If tan(A-B) =16/63, and tanA= 3/4 then show that: tanB= 5/12. Answer: You need to understand these given formulas of compound angles to be able to understand and solve these questions. #SciPiTutor #CompoundAngles #Trigonometry #Mathematics

If sin α  = 15/17 and cosß =12/13, then find the values of sin( α +ß), cos( α  +ß) and tan( α  +ß). Answer: You need to understand the given formulas of compound angles to solve these questions. #SciPiTutor #CompoundAngles #Trigonometry #Mathematics

If cosA= 1/7 and cosB = 13/14, find the values of  sin(A-B) and cos(A-B). Answer: You need to know these following things to be able to solve such questions and get the value of given compound angles. #SciPiTutor #CompoundAngles #Trigonometry #Mathematics