Tan(A+30)+cot(A-30) = 1/sin 2a - sin60   LHS   = tan(A+30) +cot(A-30)   = sin(a+30)/cos(a+30) + cos(a-30)/sin(a-30)  = sin(a+30)sin(a-30) + cos(a+30)cos(a-30)/cos(a+30)sin(a-30) taking LCM  using cos .....

  5cosθ − 20cos³θ +16cos⁵θ cosθ(5 − 20cos²θ + 16cos⁴θ)  = cosθ(5 − 20cosθcosθ + (4cosθcosθ)²)  = cosθ(5 − .....

Let θ/8 = A. So, the equation to prove will be   sec⁡2A-1sec⁡A-1= .....

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Construct two straight lines BE and CE as shown below. BC and BE are the radii of first circle and CB and CE are the radii of second circle. According to question, the radii of both circles are equal. So, BC = BE = CE Since all sides of triangle .....

Here,  Join A&S and A&R as shown in the figure. Now,  1. ∡D + ∡PAS = 180o                   [ Since, APDS is a cyclic qd.] 2. ∡C + ∡RAS = 180o  .....

Here,  1. Arc BC = Arc CD          [ Since, BC = CD is given.] 2. Arc AB + Arc BC + Arc CD = Arc CD + Arc ED  + Arc AB         [ Adding equal arcs on both sides.] 3. Arc ABCD = Arc .....

The king was the head and ruler of the state. The administration was joint and shared by the brothers. In the case of an inefficient king, the ministers and nobles took the power of the king. Sometimes, there would be a struggle between the son .....

An embankment is a wall or bank of earth or stone built to prevent a river flooding an area. As embankment are raised bank along the river, they effectively make the river deeper so it can hold more water before it .....

Ram Baran Yadav was the first person to hold FIFA world cup .....

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Here,  [√(y +1) - √(y - 1)]/ [√(y + 1)+√(y - 1)] Multiplying and dividing by √(y + 1) - √(y - 1), we get  = [√(y +1) - √(y - 1)][√(y + 1) - √(y - 1)]/ [√(y + .....

Here,  Radius = OA = 13cm Length of chord = 24cm So, AP = 24cm/2 = 12cm            [ Perpendicular drawn from the centre bisects the chord.] Now, in right angle triangle AOP,  OP = √[ .....

Here, LHS =  sec260o - tan260o          = (2)2 - (√3)3              [ Since, sec60o = 2 & tan60o = √3.]         = 4 - .....

We know, π = 180o  So, given expression becomes,       Sec245o .sec260o(cosec30o - cosec90o) = √22 . 22(2 - 1)     [ Since, using value of sec45, sec60 , cosec30 & .....

Proved.Here,  LHS = cosA/secA + sinA/cosecA          = cosA.cosA + sinA.sinA      [ Since, 1/secA = cosA & 1/cosecA = sinA.]        = cos2A + sin2A       .....

Here,  (2√3 -3√2) / (2√3 +3√2) Multiplying and dividing by (2√3 -3√2) we get, (2√3 -3√2)(2√3 -3√2)/ [(2√3 +3√2)(2√3 -3√2)] = (2√3 .....

Here, 3tan2⁡π6 + 43cos2⁡π6 - 12sec2⁡π4 - 13sin2⁡π3 We know, π = 180o, so given question becomes,  3 tan 2 ⁡30o  +  4/ 3 cos 2 ⁡30o  -  1/ 2 sec 2 ⁡45o  .....

The proper availability of electricity will help to develop industries in the country. The development of industries will also help to boos up the national economy. This will expand international trade as the development of industries focuses on .....

Here, length of highway blacktopped by Chinese = 2/5 ⨯ 110km = 44km Remaining part = 110 - 44 = 66km. Again, 5/6 part of the remaining part is done by Britrish = 5/6 ⨯ 66km = 55km. So, remaining part which is done by others = 66- 55 .....

Here,  5/(3√7 + 2√3) Multiplying and dividing by (3√7 - 2√3) = 5/(3√7 + 2√3) ⨯ (3√7 - 2√3)/(3√7 - 2√3)  = 5(3√7 - 2√3) / [ (3√7)2  - .....

Your definition about community is good. You can collect the ideas from your friends' definition .....

Some facts about morning are as follows:  - I woke up early in the morning. - The sky is bright. - The birds chirping and enjoying the cool breeze. - The dew drops falling from the leaves of the plants. - The grass is wet due to the dew .....

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Here, We need to find the value of : tan⁡π3.sin⁡π6+cos⁡π4.cos⁡π2+cos⁡π2.sin⁡π3 We know,  π = 180o. So, given expression will be,     tan60o .sin60o + cos45o cos90o + .....

Here, Amount he lends to friend  = 3/5 of total = 3/5⨯ Rs.450 = Rs.270 Now money after lending to friend with him = Rs.450 - Rs.270 = Rs.180 Amount spends to bye shirt = 2/3 of Rs.180 = Rs.120. So, the amount left with him = Rs. 180 .....

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Here,  2cosec260o + 4 sec245o + 6 cot245o Repalcing cot45o = 1, sec45o = √2 and cosce60o = 2/√3, we get = 4 (2/√3)2 + 4(√2)2 + 6(1 )2 = 8/3 + 8 + 6 Simplify and find the .....

Here,  4/3 tan260o + 3/4 sec245o - 1/2 cosec260o Repalcing tan60o = √3, sec45o = √2 and cosce60o = 2/√3, we get = 4/3 (√3)2 + 3/4(√2)2 + (2√3 )2 = 4 + 3/2 + .....

Here,  2/3 sin 260o + 3 cot260o + cot245o Repalcing sin60o = √3/2, cot60o = 1/√3 and cot 45o = 1, we get = 2/3 (√3/2)2 + 3(1/√3)2 + 12 = 1/2 + 1 + 1 Simplify and find .....

3. Multimedia system is the system having the capability to catch, store, compress, retrieve, decompresses data ie. run multimedia technology whereas multimedia technology is the technology which stores text, sound, graphics, figures and other .....

If then what are the advantages of it? Well, the advantages of good governance are mentioned in the points below: - Good governance helps to maintain a corruption-free environment in the country. - It helps to maintain peace and prosperity in the .....

Supreme Court is the apex or highest level of court in Nepal. It is also called the court of record. All of its proceedings are recorded for perpetual memory and testimony. As the guardian of the constitution, it protects and interprets the .....

If there is no good governance in the society, the following things may happen: - Corruption may occur in every sector. - Rule of law will not be maintained. - The government may not be people oriented. - The service delivery may not be quick and .....

Some of the important features of our constitution are: - The constitution has been formulated as per the aspiration of the people. - The constitution has made the provision of an independent judiciary. - There is the provision of .....

Math is both an art (a system of skills used to do calculations, devise proofs, and so on) and a science (a system of knowledge about numbers, shapes, and other abstract entities, and a way of gaining that knowledge). That is, it's both a way .....