11th Business Maths Monthly Test - 3 ( Trigonometry )

MABS Institution

11th Business Maths Monthly Test - 3 ( Trigonometry )-Aug 2020

Time : 2.00 Hours

Part - A

Generic 2 - Answer All Question

Evaluate\(\cos\left[\frac{\pi}{3}-\cos^{-1}\left(\frac{1}{2}\right)\right]\)

Simplify: sin^-1 \((\frac{1}{3})+sin^-1(\frac{2}{3})\)

Evaluate: cos 20° + cos 100° + cos 140°

Solve tan^-1(x+2)+tan^-1(2-x)=tan^-1\((\frac{2}{3})\)

Find the principal value of tan^-1(-\(\sqrt{3}\))

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

Find the values of the following trigonometric ratios. \(\sec { \left( { 390 }^{ o } \right) } \)

Find the values of the following trigonometric ratios. \(\cos { \left( { -210 }^{ o } \right) } \)

Express the following as sum or difference
2sin2\(\theta\)cos\(\theta\)

Find the value of tan 15^o

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

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

Prove that \(sin^2\left(\frac{\pi}{8}+\frac x2\right)-sin^2\left(\frac{\pi}{8}-\frac x2\right)=\frac{1}{\sqrt2}\sin x.\)

Find the degree measure corresponding to the following radian measure. -3

Part - B

Generic 3 - Answer All Question

Find the values of the following. sin 76^o cos 16^o + cos 76^o sin 16^o

Prove that \(\frac { tan5x-2sin3x+sinx }{ cos5x-cosx } =tanx\)

If three angles A, B and C are in arithmetic progression, Prove that \(cotB=\frac { sinA-sinC }{ cosC-cosA } \)

Find sin105^o + cos105^o

Find the values of the following sin (-105)°

Find the values of the following. cos 70^o cos 10^o - sin 70^o sin 10^o

Prove that: \((cos\alpha -cos\beta )^{ 2 }+(sin\alpha -sin\beta )^{ 2 }=4sin^{ 2 }\left( \frac { \alpha -\beta }{ 2 } \right) \)

Express each of the following as the sum or difference of sine or cosine:
\(sin\frac { A }{ 8 } sin\frac { 3A }{ 8 } \)

Evaluate \(\cos\left(\sin^{-1}\left(\frac{4}{5}\right)+\sin^{-1}\left(\frac{12}{13}\right)\right)\)

Prove that: \(2cos\frac { \pi }{ 13 } cos\frac { 9\pi }{ 13 } +cos\frac { 3\pi }{ 13 } +cos\frac { 5\pi }{ 13 }=0 \) .

If \(\cos { A } =\frac { 13 }{ 14 } \quad \)and \(\cos { B } =\frac { 1 }{ 7 } \) where A, B are acute angles, prove that A-B=\(\frac { \pi }{ 3 } \)

Prove that (cos \(\alpha\)+cos\(\beta\))²+ (sin\(\alpha\)+sin\(\beta\))² =cos2\(\frac{\alpha-\beta}{2}\)

If sin \(\alpha +\sin { \beta } =a\) and \(\cos { \alpha + } \cos { \beta } =b\) , then prove that \(\cos { \left( a-\beta \right) } =\frac { { a }^{ 2 }+{ b }^{ 2 }-2 }{ 2 } \)

Prove that \(2\sin^2\frac{3\pi}{4}+2\cos^2\frac{\pi}{4}+2\sec^2\frac{3\pi}{4}=10\)

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11th Business Maths Monthly Test - 3 ( Trigonometry )

MABS Institution

11th Business Maths Monthly Test - 3 ( Trigonometry )-Aug 2020

Part - A

Generic 2 - Answer All Question

Evaluate\(\cos\left[\frac{\pi}{3}-\cos^{-1}\left(\frac{1}{2}\right)\right]\)

Simplify: sin-1 \((\frac{1}{3})+sin^-1(\frac{2}{3})\)

Evaluate: cos 20° + cos 100° + cos 140°

Solve tan-1(x+2)+tan-1(2-x)=tan-1\((\frac{2}{3})\)

Find the principal value of tan-1(-\(\sqrt{3}\))

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

Find the values of the following trigonometric ratios. \(\sec { \left( { 390 }^{ o } \right) } \)

Find the values of the following trigonometric ratios. \(\cos { \left( { -210 }^{ o } \right) } \)

Express the following as sum or difference 2sin2\(\theta\)cos\(\theta\)

Find the value of tan 15o

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

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

Prove that \(sin^2\left(\frac{\pi}{8}+\frac x2\right)-sin^2\left(\frac{\pi}{8}-\frac x2\right)=\frac{1}{\sqrt2}\sin x.\)

Find the degree measure corresponding to the following radian measure. -3

Part - B

Generic 3 - Answer All Question

Find the values of the following. sin 76o cos 16o + cos 76o sin 16o

Prove that \(\frac { tan5x-2sin3x+sinx }{ cos5x-cosx } =tanx\)

If three angles A, B and C are in arithmetic progression, Prove that \(cotB=\frac { sinA-sinC }{ cosC-cosA } \)

Find sin105o + cos105o

Find the values of the following sin (-105)°

Find the values of the following. cos 70o cos 10o - sin 70o sin 10o

Prove that: \((cos\alpha -cos\beta )^{ 2 }+(sin\alpha -sin\beta )^{ 2 }=4sin^{ 2 }\left( \frac { \alpha -\beta }{ 2 } \right) \)

Express each of the following as the sum or difference of sine or cosine: \(sin\frac { A }{ 8 } sin\frac { 3A }{ 8 } \)

Evaluate \(\cos\left(\sin^{-1}\left(\frac{4}{5}\right)+\sin^{-1}\left(\frac{12}{13}\right)\right)\)

Prove that: \(2cos\frac { \pi }{ 13 } cos\frac { 9\pi }{ 13 } +cos\frac { 3\pi }{ 13 } +cos\frac { 5\pi }{ 13 }=0 \) .

If \(\cos { A } =\frac { 13 }{ 14 } \quad \)and \(\cos { B } =\frac { 1 }{ 7 } \) where A, B are acute angles, prove that A-B=\(\frac { \pi }{ 3 } \)

Prove that (cos \(\alpha\)+cos\(\beta\))2+ (sin\(\alpha\)+sin\(\beta\))2 =cos2\(\frac{\alpha-\beta}{2}\)

If sin \(\alpha +\sin { \beta } =a\) and \(\cos { \alpha + } \cos { \beta } =b\) , then prove that \(\cos { \left( a-\beta \right) } =\frac { { a }^{ 2 }+{ b }^{ 2 }-2 }{ 2 } \)

Prove that \(2\sin^2\frac{3\pi}{4}+2\cos^2\frac{\pi}{4}+2\sec^2\frac{3\pi}{4}=10\)

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Simplify: sin^-1 \((\frac{1}{3})+sin^-1(\frac{2}{3})\)

Solve tan^-1(x+2)+tan^-1(2-x)=tan^-1\((\frac{2}{3})\)

Find the principal value of tan^-1(-\(\sqrt{3}\))

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

Express the following as sum or difference
2sin2\(\theta\)cos\(\theta\)

Find the value of tan 15^o

Find the values of the following. sin 76^o cos 16^o + cos 76^o sin 16^o

Find sin105^o + cos105^o

Find the values of the following. cos 70^o cos 10^o - sin 70^o sin 10^o

Express each of the following as the sum or difference of sine or cosine:
\(sin\frac { A }{ 8 } sin\frac { 3A }{ 8 } \)

Prove that (cos \(\alpha\)+cos\(\beta\))²+ (sin\(\alpha\)+sin\(\beta\))² =cos2\(\frac{\alpha-\beta}{2}\)