a) tan35 b) - cot 35 c) - tan35 d) tan 55
2)If tan(x/2)= t, then value of (1 - t²)/(1 + t²) is
a) cos 2x b) sec x c) cosx d) tanx
3) If 0< x <π/2, then largest angle of the triangle sides are 1, sinx and cosx is
a)2π/3 - x b) π/2 c) 2π/3 d) x
4) In triangle ABC, if a²+ b²+ c²- bc - ca - ab=0, then the value of sin²A+ sin²B + sin²C is
a) 9/4 b) 4/9 c) 3√3/2 d) 3/2
5) if tanx = -4/3, then the value of sinx.
a) 2/5 b) 4/5 or -4/5 c) 4/5 but ≠ -4/5 d) -4/5 but ≠ 4/5
6) The general solution of tan 5x= tan 3x is
a) (2n +1/π b) nπ/2 c) nπ d) none
7) If tanx + secx = eˣ, then the value of cosx is
a) (eˣ - e⁻ˣ)/(eˣ + e⁻ˣ) b) (eˣ - e⁻ˣ)/2 c) 2/(eˣ - e⁻ˣ) d) 2/(eˣ + e⁻ˣ)
8) The number of integral value of k for which the equation 7 cos x + 5 sin x = 2k + 1 has a the solution. is
a) 8 b) 6 c) 7 d) 9
9) The value of (tanx + 2tan2x)/tanx is
a) less than 1
b) greater than 5
c) cannot lie witin 1 and 5
d) either less than 1 or greater than 5
10) The trigonometrical equation sinx + cosx = 2 has
a) one solution b) two solution c) infinite number of solutions d) no solution
11) The value of 3[sun⁴(3π/2 - x) + sin⁴(3π+ x)] - 2[sin⁶(π/2 + x)+ sin⁶(5π - x)] is equal to
a) 2 b) 1 c) 0 d) 4
12) In a triangle of ABC , if (b+ c)/11= (c + a)/12= (a+ b)/13, then the value of cosC is
a) 16/17 b) 17/36 c) 5/7 d) 5/6
13) The value of (sin 47 - sin 25 + sin 61 - sin11) is
a) cos 7 b) sin 7 c) 2 sin7 d) 2 cos 7
14) if in a triangle ABC, A≠ B and a cosA = b cos B, then which of the following is correct ?
a) a²= b²+ c² b) c²= a²+ b² c) b²= c²+ a² d) none
15) if m, n, p are angles such that tanm+ tan n+ tan p= tan m tan n tan p and x= cosm + i sin m, y= cos n + i sin n and z= cos p + i sin p, then the value of xyz is
a) 1 b) - 1 c) 0 d) 1 or -1
16) if sinx + sin²x = 1, then the value of (cos¹²x + 3 cos¹⁰x+ 3 cos⁸x + cos⁶x) is
a) 1 b) 4 c) 2 d) 3
17) If x = 2sin k/(1+ sin²k + cos k) then the value of (1+ sink- cosk)/(1+ sink) is
a) -x/2 b) x/2 c) x d) - x
18) The roots of the equation 1- cosx = sinx sin(x/2) are
a) nπ/4 b) 2nπ c) nπ d) nπ/2 where n belongs to Z
19) In triangle ABC, if b²= c²+ a² then the value of (tanA+ tanC) is
a) tanA tanC b) tanB c) c²/ab d) b²/ac
20) If x + y= (4n +1)π/4(where n is an integer) and x+ y is not an odd multiple of π/2, then the value of (sin2x + sin2y)/(cos2x + cos2y) is
a) 1 b) 0 c) 1 d) 1/2
21) If 1+ cosx= k where x is acute then the value of sin(x/2) is
a) √(2 -k) b) √{(2 -k)/2} c) √{(1 -k)/2} d) √{(2 +k)/2}
22) The value of the expression cos 1 cos 2 cos 3 ....cos 179 is
a) 1 b) 1/√2 c) -1/√2 d) 0
23) If ∆= a²-(b - c)², where ∆ is the area of the triangle ABC, then tanA is equal to
a) 8/17 b) 11/15 c) 15/16 d) 8/15
24) If 12cot²x - 31cosecx + 32= 0, then the value of sinx is
a) 4/5 or 3/4 b) 2/3 or -3/4 c) ±1/2 d) 1 or 3/5
25) The value of (cos⁶5- 15 cos⁴5sin² 5+ 15 cos²5 sin⁴5- sin⁶5) is equal to
a) -1/√2 b) √3/2 c) 1/√2 d) 1
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