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11th Business Maths Weekly Test - 1 ( Trigonometry )

MABS Institution

11th Business Maths Weekly Test - 1 ( Trigonometry )-Aug 2020

Time : 1.30 Hours

Part - A

Multiple Choice Question - Answer All Question

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

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

The value of \(\frac{2\tan30^o}{1+tan^230}\) is

\(\frac12\)
\(\frac{1}{\sqrt3}\)
\(\frac{\sqrt{3}}{2}\)
\(\sqrt3\)

The degree measure of \(\frac{\pi}{8}\) is

20^o60^'
22^o30^'
20^o60^'
20^o30^'

The value 4cos³40^o-3cos40^o is

\(\frac{\sqrt3}{2}\)
\(\frac{-1}{2}\)
\(\frac{1}{2}\)
\(\frac{1}{\sqrt2}\)

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

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

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

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

The value of sec A sin(270^o+A) is

-1
cos² A
sec² A
1

The value of \(\frac{1}{cosec(-45^o)}\) is

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

\(\tan\left(\frac{\pi}{4}-x\right)\) is

\(\left(\frac{1+\tan x}{1-\tan x}\right)\)
\(\left(\frac{1-\tan x}{1+\tan x}\right)\)
1-tan x
1+tan x

The value of \(\cos(-480^o)\) is

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

Part - B

Generic 2 - Answer All Question

Show that \(\tan^{-1}\left(\frac{1}{2}\right)+\tan^{-1}\left(\frac{2}{11}\right)=\tan^{-1}\left(\frac{3}{4}\right)\)

Find the values of the following cosec 15°
Evaluate the following cos\((sin^1\frac{5}{13})\)

Find the quadrants in which the terminal sides of the following angles lie.
-70c

Convert \(\frac{1}{4}\)radians into degree

Part - C

Generic 3 - Answer All Question

If tan x = 3/4 and II <x< 3II/2 then find the value of \(\sin\frac{x}{2}\) and \(\cos\frac{x}{2}\)

Prove that \(\tan { \left( { -225 }^{ o } \right) } \cot { \left( -{ 405 }^{ o } \right) } -\tan { \left( -{ 765 }^{ o } \right) } \cot { \left( { 675 }^{ o } \right) } =0\)

Prove that sin (A + 60°) + sin (A - 60°) = sin A.
Find the values of the following cos²15 - sin² 15^o

Show that \(\tan\left(\frac{\pi}{3}+x\right)\tan\left(\frac{\pi}{3}-x\right)=\frac{2\cos2x+1}{2\cos2x-1}\)

Part - D

Generic 5 - Answer All Question

If sin (y + z - x), sin (z + x - y), sin (x + y - z) are in A.P., prove that tan x, tan y, tan z are also in A. P

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 \(0<\beta<{{\pi}\over{2.}}\)

If \(\sin { A } =\frac { 3 }{ 5 } \) , find the values of cos 3A and tan 3A.
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(n+1)x sin(n+2) x+cos(n+1)xcos(n+2)x=cosx.

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