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11th Maths Weekly Test-2 ( Trigonometry )

St. Britto Hr. Sec. School - Madurai

11th Maths Weekly Test-2 ( Trigonometry )-Aug 2020

Time : 1.30 Hours

Part - A

Generic 2 - Answer All Question

In a ΔABC if a=3, b=5 and c=7, find cosA and cosB.

Convert:\(\frac{\pi}{5}\)radians to degrees.

Find the degree measure corresponding to the following radian measure; \(\frac { 7\pi }{ 3 } \)

Prove that sin 105^o + cos 105^o = cos 45^o
Prove that \({ tan }^{ -1 }\left( \frac { 1 }{ 7 } \right) +{ tan }^{ -1 }\left( \frac { 1 }{ 13 } \right) ={ tan }^{ -1 }\frac { 2 }{ 9 } \)

Prove that sin² (A + B) - sin² (A - B) = sin 2A sin 2B

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

Find the value of tan \(\frac{7\pi}{12}\).

Identify the Quadrant in which a given measure lies; -230⁰

The angles of a triangle ABC are in A.P and b:c=\(\sqrt { 3 } :\sqrt { 2 } \), find∠A.

Find the value tan (1050⁰)

Part - B

Generic 5 - Answer All Question

Solve cos x + sin x = cos 2x + sin 2x.

In \(\triangle\)ABC, Prove the following a sin \(\left( \frac { A }{ 2 } +B \right) \)=(b+c) sin \(\frac { A }{ 2 } \)

In \(\triangle\)ABC, Prove the following a (cos B + cos C) = 2 (b+c)sin² \(\frac { A }{ 2 } \)

In \(\triangle\)ABC, Prove the following \(\frac { { a }^{ 2 }-{ c }^{ 2 } }{ { b }^{ 2 } } =\frac { sin(A - C) }{ sin(A+C) } \)
If x cos \(\theta\) = y cos \(\left( \theta +\frac { 2\pi }{ 3 } \right) \) = z cos \(\left( \theta +\frac { 4\pi }{ 3 } \right) \), find the value of xy + yz + zx.

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