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11th Maths Weekly Test- 3( Trigonometry )

St. Britto Hr. Sec. School - Madurai

11th Maths Weekly Test- 3( Trigonometry )-Aug 2020

Time : 1.00 Hours

Part - A

Multiple Choice Question - Answer All Question

In a triangle ABC, sin²A+sin²B+sin²C=2, then the triangle is

equilateral triangle
isosceles triangle
right triangle
scalene triangle

If cospፀ+cosqፀ=0 and if p≠q, then ፀ is equal to (n is any integer)

\(\frac { \pi (3n+1) }{ p-q } \)
\(\frac { \pi (2n+1) }{ p-q } \)
\(\frac { \pi (n\pm 1) }{ p\pm q } \)
\(\frac { \pi (n+2) }{ p+q } \)

cos2ፀ cos2ф+sin2(ፀ-ф)-sin2(ፀ+ф) is equal to

sin2(ፀ-\(\phi \))
cos2(ፀ+\(\phi \))
sin2(ፀ-\(\phi \))
cos2(ፀ-\(\phi \))

\(\frac { cos6x+6cos4x+15cos2x+10 }{ cos5x+5cos3x+10cosx } \) equal to

cos2x
cosx
cos3x
2cosx

cos35⁰+cos85⁰+cos155⁰=

0
\(\frac { 1 }{ \sqrt { 3 } } \)
\(\frac { 1 }{ \sqrt { 2 } } \)
cos 275⁰

If sin\(\theta\) + cos\(\theta\) = 1 then sin⁶\(\theta\) + cos⁶\(\theta\) is

1
0
-1
2

In a \(\triangle\) ABC, C = 90° then the value of sin A + sin B-2_{\(\sqrt{2} cos{A\over2}cos {B\over 2}is\)}

-1
1
0
\({1\over 2}\)

The numerical value of tan^-11+tan^-12+tan^-13=

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

The value of tan 1° tan 2° tan 3°...tan 89° is

\(\infty\)
0
1
\(\sqrt{3}\)

sin²\((22{1\over 2}^o)\)is

\({\sqrt{2-\sqrt{2}}}\over2\)
\({2\sqrt{2}-1\over 4\sqrt{2}}\)
\({\sqrt{2-\sqrt{2}\over 2}}\)
none of these

If tanx =\({1\over 7}\) ,tan y = \({1\over 3}\) then x + y is:

\({\pi\over 4}\)
\({\pi\over 3}\)
\({\pi\over 2}\)
\({\pi}\)

tan 70°-tan 20°=

tan 50°
2 tan 50°
tan 70°
0

Which of the following is incorrect?

sinx=\(\frac { -1 }{ 5 } \)
cosx=1
secx=\(\frac { 1 }{ 2 } \)
tanx=20

The value of tan^-1 (1)+cos^-1(\(\frac{-1}{2}\))+sin^-1(\(\frac{-1}{2}\))

\(\frac{\pi}{4}\)
\(\frac{5\pi}{4}\)
\(\frac{3\pi}{4}\)
\(\frac{\pi}{2}\)

If the area Δ of a triangle ABC is given by Δ=a²-(b-c)² then tan\((\frac{A}{2})\)=

-1
0
\(\frac{1}{4}\)
\(\frac{1}{2}\)

The value of sin 20° sin40° sin60° sin18° is

\(\frac{-3}{16}\)
\(\frac{3}{16}\)
\(\frac{5}{16}\)
\(\frac{-5}{16}\)

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

zero
straight
co-terminal
standard

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

If A + B = 45° then tan A - tan B + tan A tan B is

2
0
1
-1

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

0
1
2
2 tan A

\(\frac { cos3x }{ 2cos2x-1 } \) is

cos x
sin x
tan x
cot x

If f(ፀ)=|sinፀ|+|cosፀ|, ፀ\(\in \)R, then f(ፀ) is in the interval

[0,2]
[1,\(\sqrt { 2 } \)]
[1,2]
[0,1]

If in a triangle ABC, ∠B=60°, then

(a-b)²=c²-ab
(b-c)²=a²-bc
(c-a)²=b²-ac
a²+b²=c²

If cosec x+cotx=\(\frac { 11 }{ 2 } \) then tanx=

\(\frac { 21 }{ 22 } \)
\(\frac { 15 }{ 16 } \)
\(\frac { 44 }{ 117 } \)
\(\frac { 117 }{ 44 } \)

The maximum value of 4sin²x+3cos²x+\(sin\frac { x }{ 2 } +cos\frac { x }{ 2 } \) is

\(4+√2\)
\(3+√2\)
\(9\)
\(4\)

59.0854^ois equal to

a) 59^o6 5^'. 44^" b) 59^o5^'6. 44^" c) 59^o5^'7. 44^" d) 59^o6^'5 . 44^"

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

In \(\triangle\)ABC, \(\hat{C}\) = 90° then a cosA + b cosB is:

2R sinB
2 sinB
0
2a sinB

If sinα+cosα=b, then sin2α is equal to

b²-1, if b≤\(\sqrt { 2 } \)
b²-1, if b>\(\sqrt { 2 } \)
b²-1, if b≥\(\sqrt { 2 } \)
b²-1, if b≥\(\sqrt { 2 } \)

The maximum value of 3 sinθ+4 cosθ is

1
3
4
5

If cos \(\alpha\)=\(\frac{3}{5}\) and cos \(\beta=\frac{5}{13}\), then

cos\((\alpha+\beta)=\frac{33}{65}\)
\(sin(\alpha+\beta)=\frac{56}{65}\)
\(sin^2\frac{(\alpha-\beta)}{2}=\frac{4}{65}\)
\(cos(\alpha-\beta)=\frac{66}{65}\)

Let f_k(x)=\(\frac { 1 }{ k } \)[sin^kx+cos^kx] where x\(\in \)R and k≥1. Then f₄(x)-f₆(x)=

\(\frac { 1 }{ 4 } \)
\(\frac { 1 }{ 12 } \)
\(\frac { 1 }{ 6 } \)
\(\frac { 1 }{ 3 } \)

A wheel is spinning at 2 radians/second. How many seconds will it take to make 10 complete rotations?

10\(\pi \) seconds
20\(\pi \) seconds
5\(\pi \) seconds
15\(\pi \) seconds

If two angles between 0^oand 360^o are conjugate if their sum equal to

a) -360^o b) 0^o c) 180^o d) 360⁰

Which of the following is not true?

sinፀ=-\(\frac { 3 }{ 4 } \)
cosፀ=-1
tanፀ=25
secፀ=\(\frac { 1 }{ 4 } \)

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