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11th Maths Monthly Test- 1 (Trigonometry)

St. Britto Hr. Sec. School - Madurai

11th Maths Monthly Test- 1 (Trigonometry) -Aug 2020

Time : 2.30 Hours

Part - A

Multiple Choice Question - Answer All Question

\(\frac{1}{360}\) of a complete rotation clockwise is

-1°
-360°
-90°
1°

Area of triangle ABC is

\(\frac{1}{2}\)ab cos C
\(\frac{1}{2}\)ab sin C
\(\frac{1}{2}\)ab cos B
\(\frac{1}{2}\)bc sin B

(secA+tanA-1)(secA-tanA+1)-2tanA=

0
1
2
2 tan A

The length of an arc of a circle of radius 5cm subtending a central angle measuring 15° is _____

\(5\pi\over\ 12\)cm
\(3\pi\over\ 12\)cm
\(7\pi\over\ 12\)cm
\(\pi\over\ 3\)cm

If \(\pi <2\theta <\frac { 3\pi }{ 2 } \), then \(\sqrt { 2+\sqrt { 2+2\quad cos4\theta } } \) equals to

-2 cosፀ
-2 sinፀ
2 cosፀ
2 sinፀ

Angle with measures 45° and -315° are __________ angles.

zero
straight
co-terminal
standard

\(\frac { 1 }{ cos{ 80 }^{ 0 } } -\frac { \sqrt { 3 } }{ sin{ 80 }^{ 0 } } \)=

\(\sqrt{2}\)
\(\sqrt{3}\)
2
4

If tanA=\(\frac { a }{ a+1 } \) and B=\(\frac { 1 }{ 2a+1 } \) then the value of A+B is

0
\(\frac { \pi }{ 2 } \)
\(\frac { \pi }{ 3 } \)
\(\frac { \pi }{ 4 } \)

The maximum value of 3 sinθ+4 cosθ is

1
3
4
5

If \(\sec { x } +\tan { x } =k\), \(cos{ x= }\)

\(\frac { { k }^{ 2 }+1 }{ 2k } \)
\(\frac { 2k }{ { k }^{ 2 }+1 } \)
\(\frac { k }{ { k }^{ 2 }+1 } \)
\(\frac { k }{ { k }^{ 2 }-1 } \)

Part - B

Generic 2 - Answer All Question

Find all the angle between 0^o and 360^o which satisfy the equation \(\sin ^{ 2 }{ \theta } =\frac { 3 }{ 4 } \)

Find the values of tan 165⁰.

if x = \(\sum _{ n=0 }^{ \infty }{ { cos }^{ 2n } } \theta ;\) y = \(y=\sum _{ n=0 }^{ \infty }{ { sin }^{ 2n } } \theta \) and z = \(\sum _{ n=0 }^{ \infty }{ { cos }^{ 2n }\theta } \) sin²ⁿ\(\theta \), 0 < \(\theta \) < \(\frac { \pi }{ 2 } \),then show that xyz = x+y+z
Hint :1+x+x²+x³+.......= \(\frac { 1 }{ 1-x } \), where \(\left| x\right| \)< 1].

Identify the Quadrant in which a given measure lies; 25⁰
Prove that cos 8 \(\theta\) cos 2 \(\theta\) = cos² 5\(\theta\) sin² 3\(\theta\)

Find the values of sin 72°.

Show that tan (45^o + A) = \(\frac { 1+\tan { A } }{ 1-\tan { A } } \)

Express each of the following product as a sum or difference. sin 40° cos 30°.

Eliminate θ from a cosθ = b and c sin θ = d, where a, b, c, d are constants.

Prove that sin (n + 1) \(\theta\) sin (n - 1) \(\theta\) + cos (n + 1) \(\theta\) cos (n - 1) \(\theta\) = cos 2 \(\theta\), \(n\epsilon Z\)

Part - C

Generic 3 - Answer All Question

Prove that \(cos\frac { B-C }{ 2 }= \frac { b+c }{ a } sin\frac { A }{ 2 } \)

Prove that sin 75^o - sin 15^o = cos 105^o + cos 15^o

Let \(\alpha,\beta\) be such that \(\pi<\alpha-\beta<3\pi.\)If \(sin\alpha+sin\beta=-\frac{21}{65}\ and\ cos\alpha+cos\beta=-\frac{27}{65}\) then find the value of \(cos\frac{\alpha-\beta}{2}\) is

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

In a \(\triangle \)if cos C=\(\frac { sinA }{ 2sinB } \)show that the triangle is isosceles.
Find x such that -\(\pi\) ≤ x ≤ \(\pi\) and cos 2x = sin x.

If sin A = \(\frac{3}{5}\) and cos B = \(\frac{9}{41}\), 0 < A < \(\frac{\pi}{2}\), 0 < B < \(\frac{\pi}{2}\). Find the value of sin (A + B)

A rope of length 12 m is given. find the largest area of the triangle formed by this rope and find the dimensions of the triangle So formed

Prove that \(\tan ^{ -1 }{ \left( \frac { x }{ \sqrt { { { a }^{ 2 }-{ x }^{ 2 } } } } \right) } =\sin ^{ -1 }{ \left( \frac { x }{ a } \right) } \)

Solve: tan²θ+(1-\(\sqrt3\))tanθ-\(\sqrt3\)=0

Part - D

Generic 5 - Answer All Question

Prove that \(\cos { 5x } =16\cos ^{ 5 }{ x } -20\cos ^{ 3 }{ x } +5\cos { x } \)

Express each of the following as a sum or difference. cos 5\(\theta\) cos 2\(\theta\)

Two Navy helicopters A and B are flying over the bay of Bengal at same altitude from the sea level to search a missing boat,pilots of both the helicopters sight the boat at the same while they are apart 10 km from each other, if the distance of the boat from A is 6 km and if the line segments AB subtends 60⁰ at the boat, find the distance of the boat from B

In \(\triangle\)ABC, Prove the following
\(\frac { asin(B-C) }{ { b }^{ 2 }-{ c }^{ 2 } } =\frac { bsin(C-A) }{ { c }^{ 2 }-{ a }^{ 2 } } =\frac { csin(A-B) }{ { a }^{ 2 }-{ b }^{ 2 } } \)
If A+B+C=\(\frac { \pi }{ 2 } \),prove the following sin2A+sin2B+sin2C=4 cosA cosB cos C

In \(\triangle\)ABC, if a = \(\sqrt { 3 } -1\), b =\(\sqrt { 3 } +1\) and 0 Find the other side and the other two angles

In a triangle ABC, prove that \({a^2+b^2\over a^2+c^2}={1+cos(A-B)cos C\over 1+cos (A-C)cos B}\)

Solve \(\sqrt{3}tan^2\theta+(\sqrt{3}-1)tan\theta-1=0\)

Find the value of sin²5° + sin²10° + sin²15° + ..... + sin²90° is

Find the values of \(\tan { \left( \alpha +\beta \right) } \), given that \(\cot { \alpha } =\frac { 1 }{ 2 } ,\alpha \epsilon \left( \pi ,\frac { 3\pi }{ 2 } \right) and\quad \sec { \beta } =-\frac { 5 }{ 3 } ,\beta \epsilon \left( \frac { \pi }{ 2 } ,\pi \right) \)

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