Properties of triangle

Properties of triangle | free study material for IIT-JEE , NDA and Airforce | SAT | CBSE | UPSC

⚫ Relation between sides and angles
⚪ The law of sines or sine rule : The sides of the triangle are proportional to the sines of the angles opposite to them

⚫ The law of cosine or cosine Law :

⚪ Projection Formula : a = b.cosC + c.cosB
b = c.cosA + a.cosC
c = a.cosB + b.cosA

⚫ Law of tangents :

⚫ Area of triangle

⚫ Half angle Formulae :

Practice set 1 Practice set 2

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Measurement of Angle ,Trigonometric Ratios and equation | free study Material for IIT-JEE , NDA and Airforce | SAT | CBSE

Measurement of Angle ,Trigonometric Ratios and equation ⚫Relation Between Degree and Radians ⚫ Relation Between Trigonometrical Ratios and Right Angled Triangle Side ⚫ Relation Between Trigonometrical Ratios sinθ.cosecθ = 1 tanθ.cotθ = 1 cosθ.secθ = 1 tanθ = sinθ/cosθ cotθ = cosθ/sinθ ⚫ Fundamental trigonometric Identities : sin 2 θ + cos 2 θ = 1 tan 2 θ + 1 = sec 2 θ 1 + cot 2 θ = cosec 2 θ ⚫ Trigonometrical ratios for various angles ⚫ Formula For the trigonometric ratios of sum and difference of two angles sin(A+B) = sinA cosB + cosA sinB sin(A-B) = sinA cosB - cosA sinB cos(A+B) = cosA cosB - sinA sinB cos(A-B) = cosA cosB + sinA sinB sin(A+B).sin(A-B) = sin 2 A - sin 2 B = cos 2 B - cos 2 A cos(A+B).cos(A-B) = cos 2 A - sin 2 B = cos 2 B - sin 2 A ⚫ Formulae to tran...

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Start the test Question no. 1 Let z, w be complex numbers such that z + i w =0 and arg zw =π . Then arg z equals π/4 5π/4 3π/4 π/2 Question no. 2 If z and w are two non-zero complex number such that |zw|=1, and Arg (z)-Arg(w)=π/2 , then z¯w is equal to 1 -1 -i i Question no. 3 If |z+4|<= 3, then the maximum value of |z+1| is 4 10 6 0 Question no. 4 The conjugate of complex number is 1/(i-1), then that complex number is 1/(i+1) -1/(i+1) 1/(i-1) -1/(i-1) Question no. 5 What are the square roots of -2i ? ∓(1+i) ∓(1-i) ∓i ∓1 Question no. 6 What is the value of the sum of i 2i -2i 1+i Question no. 7 What is the number of distinct solution of the equation z 2 + |z| = 0 (where z i...

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Practice question On Eigen values and Eigen vectors Linear Algebra | Matrix algebra | GATE | UPSC | IES | Engineering

Linear Algebra Question no. 1 What are the eigen values of ? looks_one 1,4 looks_two 2,3 looks_3 0,5 looks_4 1,5 Answer Option looks_3 0,5 Solution Solution : ( 4 - λ)(1 - λ) - 4 = 0 λ 2 - 5λ + 4 - 4 = 0 λ 2 - 5λ = 0 λ(λ - 5) = 0 λ = 0 , 5 Question no. 2 What is the eigenvalues of the matrix ? looks_one 1, 4 ,4 looks_two 1 , 4 ,-4 looks_3 3 , 3 ,3 looks_4 1 , 2 ,6 Answer option looks_one 1, 4 ,4 Solution Solution : ( 3 - λ )[(3-λ) 2 -1] + 1(-3 + λ -1 ) - 1(1+3 -λ) = 0 ( 3 - λ )(9 + λ 2 - 6λ -1 ) + 2( λ - 4 ) = 0 ( 3 - λ )( λ 2 - 6λ + 8 ) + 2( λ - 4 ) = 0 ( 3 - λ )( λ - 4)( λ - 2) + 2( λ - 4 ) = 0 (λ - 4) [( 3 - λ )( λ - 2) + 2 ] = 0 (λ - 4) (λ 2 - 5λ + 4) = 0 (...

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Calculus Question no. 1 If f(x) = , then will be [2006 , marks 2] looks_one -1/3 looks_two 5/18 looks_3 0 looks_4 2/5 Answer Option looks_two 5/18 Solution Solution : Question no. 2 [ 2007 , marks 1 ] looks_one 0.5 looks_two 1 looks_3 2 looks_4 undefined Answer option looks_one 0.5 solution Solution : Question no. 3 What is the value of [ 2007 , marks 2 ] looks_one 0 looks_two 1/6 looks_3 1/3 looks_4 1 Answer Option looks_two 1/6 Solution Solution : Question no. 4 The value of : [ 2008 , 1 Mark ] looks_one 1/16 looks_two 1/12 looks_3 1/8 looks_4 1/4 Answer option looks_two 1/12 Solution Solution : Question no. 5 The value of : [2008 , 1 Mark] looks_one 1 looks_two -1 looks_3 ∞ looks_4 -∞ Answer Option looks_one 1 Solution Solution : Question no. 6 ...

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Complex Number | free study material for IIT-JEE , NDA and Airforce

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