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11th Business Maths Monthly Test - 2 ( Trigonometry )

MABS Institution

11th Business Maths Monthly Test - 2 ( Trigonometry )-Aug 2020

Time : 2.30 Hours

Part - A

Multiple Choice Question - Answer All Question

The value of \(\sin 28^o\cos 17^o+\cos 28^o\sin 17^o\) is

\(\frac{1}{\sqrt2}\)
1
\(\frac{-1}{\sqrt2}\)
0

The value of 1-2sin²45^o is

1
\(\frac{1}{2}\)
\(\frac14\)
0

If \(\tan A=\frac{1}{2}\) and \(\tan B=\frac{1}{3}\) then tan(2A+B) is equal to

1
2
3
4

\(\sin\left(\cos^{-1}\frac{3}{5}\right)\) is

\(\frac{3}{5}\)
\(\frac{5}{3}\)
\(\frac{4}{5}\)
\(\frac{5}{4}\)

If \(\sin A=\frac{1}{2}\) then \(4\cos^3A-3\cos A\) is

1
0
\(\frac{\sqrt3}{2}\)
\(\frac{1}{\sqrt{2}}\)

The value of cos²45^o-sin²45^o is

\(\frac{\sqrt3}{2}\)
\(\frac{1}{2}\)
0
\(\frac{1}{\sqrt{2}}\)

\(\left(\frac{\cos x}{cosec x}\right)-\sqrt{1-\sin^2x}\sqrt{1-\cos^2x}\) is

cos²x-sin²x
sin²x-cos²x
1
0

The value of sin 15^o cos 15^o is

1
\(\frac{1}{2}\)
\(\frac{\sqrt3}{2}\)
\(\frac{1}{4}\)

If sin A+ cos A=1, then sin 2A is equal to

1
2
0
\(\frac{1}{2}\)

The radian measure of 37^o30^' is

\(\frac{5\pi}{24}\)
\(\frac{3\pi}{24}\)
\(\frac{7\pi}{24}\)
\(\frac{9\pi}{24}\)

Part - B

Generic 2 - Answer All Question

Evaluate the following cos\((sin^1\frac{5}{13})\)

Express \(\tan ^{ -1 } \left[ \frac { \cos x }{ 1-\sin x } \right] ,-\frac { \pi }{ 2 } <x<\frac { 3\pi }{ 2 } \) in the simplest form

Find the degree measure corresponding to the following radian measure. \(\frac { 9\pi }{ 5 } \)

Find the values of the following trigonometric ratios. \(\sin { { 300 }^{ o } } \)

Find the quadrants in which the terminal sides of the following angles lie.
-320^o

Find the value of \(\cos\left(\frac{5\pi}{12}\right)\)

If A, B, C, D are angles of a cyclic quadrilateral, prove that \(\cos { A } +\cos { B } +\cos { C } +\cos { D } =0\)

Part - C

Generic 3 - Answer All Question

Prove that 2 tan 80° = tan 85° - tan 5°.

Prove that \(\frac{\sin(x+y)}{\sin(x-y)}=\frac{\tan x+\tan y}{\tan x-\tan y}\)

Find the values of each of the following trigonometric ratios.
tan(- 1215^o)

If tan(x + y) = 42 and x = tan–1(2), then find y

Prove that \(\sec { \left( \frac { 3\pi }{ 2 } -\theta \right) } \sec { \left( \theta -\frac { 5\pi }{ 2 } \right) } +\tan { \left( \frac { 5\pi }{ 2 } +\theta \right) } \tan { \left( \theta -\frac { 5\pi }{ 2 } \right) } =-1\)

Express each of the following as the sum or difference of sine or cosine:
cos(60⁰+A)sin(120⁰+A)

Express each of the following as the sum or difference of sine or cosine:
\(cos\frac { 7A }{ 3 } sin\frac { 5A }{ 3 } \)

Part - D

Generic 5 - Answer All Question

Prove that \(\frac{\cos4x+\cos3x+\cos2x}{\sin4x+\sin3x+\sin2x}=\cot3x\)

If tan \(\alpha={{1}\over{7}},\sin\beta={{1}\over{\sqrt{10}}},\) Prove that \(\alpha+2\beta={{\pi}\over{4}}\) where \(0<\alpha<{{\pi}\over{2}}\) and \(0<\beta<{{\pi}\over{2.}}\)

Prove that \(\frac { \sin { \left( { 180 }^{ o }+A \right) \cos { \left( { 90 }^{ o }-A \right) \tan { \left( { 270 }^{ o }-A \right) } } } \quad \quad }{ \sec { \left( { 540 }^{ o }-A \right) \cos { \left( { 360 }^{ o }+A \right) \ cosec { \left( { 270 }^{ o }+A \right) } } } } =-\sin { A } \cos ^{ 2 }{ A } \)

Prove that cos² A +cos²(A+120^o)+ cos²(A-120^o)=\(\frac{3}{2}\)

If cosec A + sec A = cosec B + sec B, prove that cot\(\left( \frac { A+B }{ 2 } \right) \)=tanA tanB
If cosA =\(\frac{4}{5}\)and cosB =\(\frac{12}{13}\),\(\frac{3\pi}{3}\)\(\pi\), find the value of cos(A+B).

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

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