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- Special Thanks goes to our community manager Adam Kosh for assisting me with figuring out the Math Formula !/lesson/pages/2266-how-much-distance-will-affect-joyce-and-harrys-love/photos/5292-lar…
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Introductory Trigonometry
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- Introduction to Trigonometry Trigonometry, or “trig” as all the cool guys call it, is the branch of mathematics that deals with triangles, especially right-angled ones but regular ones too. It specifically looks for relati...
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Find the each of the length?
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- Lesson 11.1The centers of the two circles are the points P and Q. The radius of circle P is 8; the radius of circle Q is 12. Find each distance. a) SQ b)...
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- Friends, in this lesson I am going discuss about the “Sine Rule” and the “Extended Rule of Sine” which are quite simple rules to prove but the questions based on these rules, sometimes, may be a bit confusing. So ...
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Sine Rule and Practice Problems
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- For more information regarding this concept, I suggest you to go through the lesson Sine Rule & Practice Problems
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- Ques: 6 Let a, b, c, d be numbers in the interval [0,\pi] such that\sin a+7 \sin b=4(\sin c+2 \sin d),\cos a+7 \cos b=4(\cos c+2 \cos d).Prove that 2 \cos(a-d)=7 \cos(b-c). Solution: %{font-family:verdana}Rewrite the two given equalit...
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- Arithmetic–Geometric Means Inequality If n is a positive integer and a_1,a_2,\cdots , a_n are non-negative real numbers, then \frac {1}{n}\overset {n}{\underset {i=1}{\sum}}a_i\underline > (a_1a_2\cdots a_n)^{1/n}, with equal...
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- Law of Cosines In a triangle ABC,%{font-family:verdana}|CA|2=|AB|2+|BC|2-2|AB|.|BC|\cos \angle ABC,% and analogous equations hold for |AB|2 and |BC|2. Median formula This is also called the length of the median formula. Let AM be a me...
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- Ques: 1 Prove that 1-\cot 230=\frac {2}{1-\cot 220} First Solution: We will show that(1-\cot 30)(1-\cot 220)=2 Indeed, by the addition and subtraction formulas, we obtain %{font-family:verdana}(1-\cot 230)(1-\cot 220)=\Big (1...
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- %{font-family:verdana;font-size:17px;color:#150577}Ques: 16 Let ABC be a triangle. Prove that(a) \quad \sin \frac {A}{2}\sin \frac {B}{2} \sin \frac {C}{2}\underline < \frac {1}{8};(b) \quad \sin2 \frac {A}{2}\sin2 \frac {B}{2} \sin2 ...
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- Hi this is IIT JEE-2009 information broucher.The information broucher is available on right bottom of the “published in ” in the sane page.
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- Ques: 18 In triangle ABC, show that(a) \quad 4R=\frac {abc}{[ABC]};(b) \quad 2R2 \sin A\sin B \sin C=[ABC];(c) \quad 2 R \sin A\sin B \sin C=r(\sin A+\sin B+\sin C);(d) \quad r=4R \sin\frac {A}{2}\sin \frac {B}{2} \sin \frac {C}{2};(e) \...
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- %{font-family:verdana;font-size:17px;color:#150577}Ques: 21 Let ABC be a triangle. Prove that(a) \quad \cos A\cos B \cos C \underline < \frac {1}{8};(b) \quad \sin A\sin B \sin C \underline <\frac {3\sqrt {3}}{8};(c) \quad \sin A+\...
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- Ques: 25 Show that one can use a composition of trigonometry buttons such as, \sin,\cos,\tan,\sin,\cos{-1}, and \tan{-1,} to replace the broken reciprocal button on a calculator. Solution: %{font-family:verdana}Because \cos{1}\sin \th...
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- Ques: 31 If \sin \alpha \cos \beta=-\frac {1}{2}, what are the possible values of \cos \alpha \sin \beta ? Solution: %{font-family:verdana}Note that \sin(\alpha \beta)=\sin \alpha \cos \beta +\cos \alpha \sin \beta =- \frac {1}{2}\cos...
