Important Trigonometry Math for SSC
ত্রিকোণমিতি ম্যাথ এর কিছু প্রশ্ন (Important Trigonometry Math) দেওয়া হলো। এই গুলো সেন্ট্রাল এসএসসি পরিক্ষার জন্য খুব গুরুত্বপূর্ণ।
গণিত- ত্রিকোণমিতি-মিসলেনিয়াস টাইপ -সেট ১
1)If sec Ө –cos Ө = (3/2) where Ө is a positive acute triangle then the value of sec Ө is
A) -(1/2)
B) 2
C) 0
D) 1
2)If tan (5x -10°) = cot (5y + 20°) the value of (x+y) is
A) 15°
B) 24°
C) 20°
D) 16°
3)If sinӨ + sin2 Ө = 1, then the value of
cos12 Ө +3 cos10 Ө+3cos8 Ө+ cos 6 Ө -1 is
A) 1
B) 3
C) 0
D) 2
4)The value of tan 11° tan 17° tan 79° tan 73° is
A) (1/2)
B) 1
C) (1/√2)
D) 0
5)The value of (1 + sec 20° +cot 70°) (1-cosec 20° +tan 70°)
is equal to
A) 0
B) 2
C) 0
D) 1
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Important Trigonometry Math-Answers
1.B)
1/cos Ө –cos Ө= 3/2
2(1-cos 2Ө) =3 cos Ө
2 cos 2 Ө + 3 cos Ө -2=0
2 cos2 Ө + 4 cos Ө –cos Ө-2 =0
2cos(cos Ө +2)-1(cos Ө + 2) =0
(cosӨ + 2) (2cos Ө -1) = 0
Cos Ө =1/2, cos Өǂ-2
∴sec Ө =2
TRICKS
Put value Ө=60°
So you will get sec Ө –cos Ө=sec 60°-cos 60 °=2-1/2=3/2(proved)
∴ sec Ө=sec 60°=2
2.D)
Tan (5x-10°) = tan {90°-(5y +20°)}
5x-10°=70°-5y
5x +5y =80°
∴x + y = 16°
3.C)
sin Ө = 1-sin2 Ө
sin Ө = cos2 Ө ………..(i)
cos12 Ө +3 cos10 Ө+3cos8 Ө+ cos 6 Ө -1
= (cos4 Ө)3 + 3 (cos4 Ө)2 cos2 Ө + 3 cos4 Ө (cos2 Ө)2 + (cos2 Ө)3 -1
= (cos4 Ө + cos2 Ө)3-1
= (sin2 Ө + cos2 Ө)3-1 from equation (i)
So, (1)3-1=0
TRICKS
cos12 Ө +3 cos10 Ө+3cos8 Ө+ cos 6 Ө (This is a3+b3 form)
So always ans. be 1
Next 1-1=0
4.B) TRICKS
always ans. is 1
5.B) TRICKS
always ans. is 2
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6) If sin Ө + cos Ө = (17/13), 0<Ө< 90°, then the value of sin Ө- cos Ө is
A) (5/17)
B) (3/19)
C) (7/10)
D) (7/13)
7)The least value of (4 cosec2Ө + 9 sin2Ө) is
A) 12
B) 19
C) 25
D) 7
8)The value of (tan 35° tan 45° tan 55°)
A) (1/2)
B) 2
C) 0
D) 1
9)If cos A + cos2A = 1, then sin2 A + sin4A is equal to
A)0
B) (1/2)
C) 0
D) 1
10)If sin(x+y) = cos [3(x+y)], then the value of tan [2(x+y)] is
A) √3
B) 1
C) 0
D) 1/√3
11)If cos2Ө-sin2Ө = 1/3, where 0 < Ө ≤ 90°, then the value of cos4Ө -sin4Ө is
A) (1/3)
B) (2/3)
C) (1/9)
D) (2/9)
12)If sec x + cos x= 3, then tan2x – sin2x is
A) 5
B) 12
C) 9
D) 4
13)If the value of x sin3Ө + y cos3Ө = sinӨ + cosӨǂ0 and x sinӨ -ycosӨ=0 ,
Then value of (x2 + y2) is
A) 1
B) sinӨ-cosӨ
C) sinӨ + cosӨ
D) 0
14)If sin 2Ө= (1/2), then the value of cos (75°-Ө) is
A) 1
B) 1/2
C) (√3/2)
D) (1/√2)
15)If tan Ө.tan2Ө=1, then the value of sin22Ө + tan22Ө is equal to
A)3/4
B)10/3
C)15/4
D)3
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=7/13
7.A) Tricks
2.√4.√9 = 12
8.D) Tricks
Always value will be 1
9.D) Tricks
Always value will be 1
10.B) Tricks
x+ y +3x+3y = 90°
4x + 4y= 90°
2x+2y = 45°
Tan (2x +2y) = tan 45°=1
11.A) Tricks
Always value (1/3) will be answer
12.A) Tricks
Required answer = (32-2-2) = 5
13.A) Tricks
After solving you will always get x= cosӨ, y= sinӨ
So x2+y2=sin2Ө + cos2Ө=1
14.B) Sin 2Ө=sin60° and 2Ө=30°
So Ө=15°.Hence cos60°= (1/2)
15.C)
(Ө+2Ө) =90°
Ө=30°
sin22Ө + tan22Ө
=sin260° + tan260°
= (15/4)
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