11th Maths Monthly Test- 4 (Trigonometry)

St. Britto Hr. Sec. School - Madurai

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

Time : 2.00 Hours

Part - A

Generic 2 - Answer All Question

Prove that \(\frac { cos(2\pi +x)cosec(2\pi +x)tan\left( \frac { \pi }{ 2 } +x \right) }{ sec\left( \frac { \pi }{ 2 } +x \right) cos.cot(\pi +x) } \)=1

Find the value of \(cot(\frac{-15\pi}{4})\).

Find the general solution of tan \(\theta\) = \(\sqrt{3}\)

Prove that sin (A + B) sin (A - B) = sin² A - sin² B.

Find the principal value of sin^-1\(({\sqrt{3}\over2})\)

Find (1 + tan A + sec A) (1 + cot A -cosec A).

A fighter jet has to hit a small target by flying a horizontal distance. When the target is sighted, the pilot measures the angle of depression to be 30⁰. If after 100km, the target has an angle of depression of 45⁰, how far is the target from the fighter jet at that instant?

If \(\cot { x\left( 1+sinx \right) } =4m\) and \(\cot { x\left( 1-sinx \right) } =4n\) , prove that \({ \left( { m }^{ 2 }-{ n }^{ 2 } \right) }^{ 2 }=mn\)

Find the values of cos 2A, A lies in the first quadrant, when cos A = \(\frac{15}{17}\)

Find the values of cos(300°).

Part - B

Generic 3 - Answer All Question

In a \(\triangle ABC\);\(a=2\sqrt 2,b=2\sqrt 3\) and C=75⁰, find the other side and the angles.

Find the principal solution of cosec\(\theta\)= -2.

Derive cosine formula using the law of sines in a \(\triangle ABC.\)

Prove that \(cos\left( \frac { \pi }{ 4 } -A \right) cos\left( \frac { \pi }{ 4 } -B \right) -sin\left( \frac { \pi }{ 4 } -A \right) sin\left( \frac { \pi }{ 4 } -B \right) \)

Prove \(\frac { cosA }{ a } +\frac { cosB }{ b } +\frac { cosC }{ c } =\frac { { a }^{ 2 }+{ b }^{ 2 }+{ c }^{ 2 } }{ 2abc } \)

Part - C

Generic 5 - Answer All Question

If \(\sin { x } =\frac { 15 }{ 17 } \) and \(\cos {y } =\frac { 12 }{ 13 } \), 0 < x < \(\frac{\pi}{2}\), 0 < y < \(\frac{\pi}{2}\), find the value of cos (x - y)

Find the values of other five trigonometric functions for the following
sin \(\theta\) = -\(\frac { 2 }{ 3 } \) \(\theta\)= lies in the IV quadrant

A circular metallic plate of radius 8 cm and thickness 6 mm is melted and molded into a pie ( s sector of the circle with thickness) of radius 16 cm and thickness 4 mm. find the angle of the sector

Prove that \(\frac { sinx+sin3x+sin5x+sin7x }{ cosx+cos3x+cos5x+cos7x } =tan4x\)

Prove that (i) cos 20° cos 40° cos 80° \(=\frac{1}{8}\)

Comment

Add Comment

InstaQB

Institutions

12th Standard English Medium

12th Standard Tamil Medium

11th Standard English Medium

11th Standard Tamil Medium

10th Standard English Medium

9th Standard English Medium

8th Standard English Medium

7th Standard English Medium

Class XII

Class XI

12Th Standard

11Th Standard

10Th Standard

9Th Standard

11th Maths Monthly Test- 4 (Trigonometry)

St. Britto Hr. Sec. School - Madurai

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

Part - A

Generic 2 - Answer All Question

Prove that \(\frac { cos(2\pi +x)cosec(2\pi +x)tan\left( \frac { \pi }{ 2 } +x \right) }{ sec\left( \frac { \pi }{ 2 } +x \right) cos.cot(\pi +x) } \)=1

Find the value of \(cot(\frac{-15\pi}{4})\).

Find the general solution of tan \(\theta\) = \(\sqrt{3}\)

Prove that sin (A + B) sin (A - B) = sin2 A - sin2 B.

Find the principal value of sin-1\(({\sqrt{3}\over2})\)

Find (1 + tan A + sec A) (1 + cot A -cosec A).

A fighter jet has to hit a small target by flying a horizontal distance. When the target is sighted, the pilot measures the angle of depression to be 300. If after 100km, the target has an angle of depression of 450, how far is the target from the fighter jet at that instant?

If \(\cot { x\left( 1+sinx \right) } =4m\) and \(\cot { x\left( 1-sinx \right) } =4n\) , prove that \({ \left( { m }^{ 2 }-{ n }^{ 2 } \right) }^{ 2 }=mn\)

Find the values of cos 2A, A lies in the first quadrant, when cos A = \(\frac{15}{17}\)

Find the values of cos(300°).

Part - B

Generic 3 - Answer All Question

In a \(\triangle ABC\);\(a=2\sqrt 2,b=2\sqrt 3\) and C=750, find the other side and the angles.

Find the principal solution of cosec\(\theta\)= -2.

Derive cosine formula using the law of sines in a \(\triangle ABC.\)

Prove that \(cos\left( \frac { \pi }{ 4 } -A \right) cos\left( \frac { \pi }{ 4 } -B \right) -sin\left( \frac { \pi }{ 4 } -A \right) sin\left( \frac { \pi }{ 4 } -B \right) \)

Prove \(\frac { cosA }{ a } +\frac { cosB }{ b } +\frac { cosC }{ c } =\frac { { a }^{ 2 }+{ b }^{ 2 }+{ c }^{ 2 } }{ 2abc } \)

Part - C

Generic 5 - Answer All Question

If \(\sin { x } =\frac { 15 }{ 17 } \) and \(\cos {y } =\frac { 12 }{ 13 } \), 0 < x < \(\frac{\pi}{2}\), 0 < y < \(\frac{\pi}{2}\), find the value of cos (x - y)

Find the values of other five trigonometric functions for the following sin \(\theta\) = -\(\frac { 2 }{ 3 } \) \(\theta\)= lies in the IV quadrant

A circular metallic plate of radius 8 cm and thickness 6 mm is melted and molded into a pie ( s sector of the circle with thickness) of radius 16 cm and thickness 4 mm. find the angle of the sector

Prove that \(\frac { sinx+sin3x+sin5x+sin7x }{ cosx+cos3x+cos5x+cos7x } =tan4x\)

Prove that (i) cos 20° cos 40° cos 80° \(=\frac{1}{8}\)

Comment

Other Study material

11th Maths Monthly Test -2( Differential Calculus

11th Maths Monthly Test - 4 ( Introduction to prob

11th Maths Weekly Test - 1 ( Differential Calculus

11th Maths Monthly Test - 4 ( Differential Calcul

11th Maths Monthly Test - 3( Differential Calculu

11th Maths Weekly Test - 3 ( Vector Algebra )

11th Maths Weekly Test -4 ( Vector Algebra )

11th Maths Monthly Test- 1 (Vector Algebra )

11th Maths Monthly Test -2( Vector Algebra )

11th Maths Monthly Test - 3 ( Vector Algebra )

11th Maths Monthly Test - 4 ( Vector Algebra )

11th Maths Weekly Test -1( Differential Calculus

11th Maths Weekly Test-2 ( Differential Calculus -

11th Maths Weekly Test - 3 ( Differential Calculus

11th Maths Weekly Test - 4 ( Differential Calculus

Tamilnadu Stateboardszs - Class

Prove that sin (A + B) sin (A - B) = sin² A - sin² B.

Find the principal value of sin^-1\(({\sqrt{3}\over2})\)

A fighter jet has to hit a small target by flying a horizontal distance. When the target is sighted, the pilot measures the angle of depression to be 30⁰. If after 100km, the target has an angle of depression of 45⁰, how far is the target from the fighter jet at that instant?

In a \(\triangle ABC\);\(a=2\sqrt 2,b=2\sqrt 3\) and C=75⁰, find the other side and the angles.

Find the values of other five trigonometric functions for the following
sin \(\theta\) = -\(\frac { 2 }{ 3 } \) \(\theta\)= lies in the IV quadrant