11th Business Maths Monthly Test - 4 ( Trigonometry )

MABS Institution

11th Business Maths Monthly Test - 4 ( Trigonometry )-Aug 2020

Time : 2.00 Hours

Part - A

Generic 5 - Answer All Question

If cosA+cosB=\(\frac { 1 }{ 2 } \) and sinA+sinB=\(\frac { 1 }{ 4 } \), prove that tan\(\left( \frac { A+B }{ 2 } \right) =\frac { 1 }{ 2 } \)

Prove that cot x cot 2x - cot 2x cot 3x - cot 3x cot x = 1.

Prove that \({ cot }^{ -1 }\left[ \frac { \sqrt { 1+sinx } +\sqrt { 1-sinx } }{ \sqrt { 1+sinx } -\sqrt { 1-sinx } } \right] =\frac { x }{ 2 } \) where \(x\in \left( 0,\frac { \pi }{ 4 } \right) \)

Prove that \(\tan { \left( \pi +x \right) } \cot { \left( x-\pi \right) } -\left( \cos { \left( 2\pi -x \right) } \cos { \left( 2\pi +x \right) } \right) =\sin ^{ 2 }{ x } \)

If \(\sin A=\frac35\) where \(0<A<\frac { \pi }{ 2 } \) and \(cosB=\frac { -12 }{ 13 } ,\pi <A<\frac { 3\pi }{ 2 } \) find the value of
\(\tan(A-B)\)

If \(\sin { A } =\frac { 3 }{ 5 } \) where\(0<A<\frac { \pi }{ 2 } \) and \(\cos { B } =\frac { -12 }{ 13 } \) , \(\pi <A<\frac { 3\pi }{ 2 } \) , find the values of the following sin (A - B)

Find the value of tan \(\left( {{\pi}\over{8}}\right).\)

Prove that cos 20° cos 40° cos 60° cos 80⁰=\(\frac { 1 }{ 16 } \)

If \(\sin A=\frac35\) where 0< A and cos B= -12/13 ,II <A<3II/2 find the value of
\(\cos (A+B)\)

if \(\cot { \alpha } =\frac { 1 }{ 2 } ,\sec { \beta } =\frac { -5 }{ 3 } \) where \(\pi <\alpha <\frac { 3\pi }{ 2 } \)and,\(\frac { \pi }{ 2 } <\beta <\pi \) find the value of \(\tan { \left( \alpha +\beta \right) } \) State the quadrant in which \(\left( \alpha +\beta \right) \) terminates.

Prove that (sin 3x + sin x) sin x + (cos 3x - cos x) cos x = 0.

Prove that cos²2x-cos²6x = sin 4x.sin 8x

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11th Business Maths Monthly Test - 4 ( Trigonometry )

MABS Institution

11th Business Maths Monthly Test - 4 ( Trigonometry )-Aug 2020

Part - A

Generic 5 - Answer All Question

If cosA+cosB=\(\frac { 1 }{ 2 } \) and sinA+sinB=\(\frac { 1 }{ 4 } \), prove that tan\(\left( \frac { A+B }{ 2 } \right) =\frac { 1 }{ 2 } \)

Prove that cot x cot 2x - cot 2x cot 3x - cot 3x cot x = 1.

Prove that \({ cot }^{ -1 }\left[ \frac { \sqrt { 1+sinx } +\sqrt { 1-sinx } }{ \sqrt { 1+sinx } -\sqrt { 1-sinx } } \right] =\frac { x }{ 2 } \) where \(x\in \left( 0,\frac { \pi }{ 4 } \right) \)

Prove that \(\tan { \left( \pi +x \right) } \cot { \left( x-\pi \right) } -\left( \cos { \left( 2\pi -x \right) } \cos { \left( 2\pi +x \right) } \right) =\sin ^{ 2 }{ x } \)

If \(\sin A=\frac35\) where \(0<A<\frac { \pi }{ 2 } \) and \(cosB=\frac { -12 }{ 13 } ,\pi <A<\frac { 3\pi }{ 2 } \) find the value of \(\tan(A-B)\)

If \(\sin { A } =\frac { 3 }{ 5 } \) where\(0<A<\frac { \pi }{ 2 } \) and \(\cos { B } =\frac { -12 }{ 13 } \) , \(\pi <A<\frac { 3\pi }{ 2 } \) , find the values of the following sin (A - B)

Find the value of tan \(\left( {{\pi}\over{8}}\right).\)

Prove that cos 20° cos 40° cos 60° cos 800=\(\frac { 1 }{ 16 } \)

If \(\sin A=\frac35\) where 0< A and cos B= -12/13 ,II <A<3II/2 find the value of \(\cos (A+B)\)

if \(\cot { \alpha } =\frac { 1 }{ 2 } ,\sec { \beta } =\frac { -5 }{ 3 } \) where \(\pi <\alpha <\frac { 3\pi }{ 2 } \)and,\(\frac { \pi }{ 2 } <\beta <\pi \) find the value of \(\tan { \left( \alpha +\beta \right) } \) State the quadrant in which \(\left( \alpha +\beta \right) \) terminates.

Prove that (sin 3x + sin x) sin x + (cos 3x - cos x) cos x = 0.

Prove that cos22x-cos26x = sin 4x.sin 8x

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Tamilnadu Stateboardszs - Class

If \(\sin A=\frac35\) where \(0<A<\frac { \pi }{ 2 } \) and \(cosB=\frac { -12 }{ 13 } ,\pi <A<\frac { 3\pi }{ 2 } \) find the value of
\(\tan(A-B)\)

Prove that cos 20° cos 40° cos 60° cos 80⁰=\(\frac { 1 }{ 16 } \)

If \(\sin A=\frac35\) where 0< A and cos B= -12/13 ,II <A<3II/2 find the value of
\(\cos (A+B)\)

Prove that cos²2x-cos²6x = sin 4x.sin 8x