Trigonometric Functions - Online Test
Q1. The largest value of sin θcosθ is
Answer : Option B
Explaination / Solution:
sinθcosθ=12.2sinθcosθ=12.sin2θButthemaximumvalueofsin2θis1.Sothemaximumvalueofsinθcosθ=12
Q2.
If then is equal to
Answer : Option C
Explaination / Solution:
Q3.
The equation (cos p – 1) + (cos p) x + sin p = 0, where x is a variable, has real roots. Then the interval of p may be any one of the following:
Answer : Option B
Explaination / Solution:
Q4. In a triangle ABC, a = 13, b = 14, c = 15; then the radius of the incircle r of triangle ABC=
Answer : Option C
Explaination / Solution:
Q5. If sin = 2, then
Answer : Option D
Explaination / Solution:
Q6. The value of tan - cot is equal to
Answer : Option A
Explaination / Solution:
Q7. In a triangle ABC, cosec A (sin B cos C + cos B sin C) equals
Answer : Option D
Explaination / Solution:
cosecA(sinBcosC+cosBsinC)=cosecA.sin(B+C)[∵A+B+C=π]=sin(B+C)sinA=sin(π−A)sinA=sinAsinA=1
Q8. If the angles of at triangle are in the ratio 1 : 2 : 3, then the sides are in the ratio
Answer : Option B
Explaination / Solution:
Q9. Let the angles A, B, C of be in A.P. and let b: c:: then the angle A is
Answer : Option D
Explaination / Solution:
Q10.
cot = sin 2 n , n integer) if equals
Answer : Option B
Explaination / Solution:
sin2θ=cotθ⇒2sinθcosθ=sinθcosθ⇒cosθ(2sinθ−1sinθ)=0⇒−cosθ(1−2sin2θ)=0⇒−cosθ.cos2θ=0⇒cosθ=cosπ20rcos2θ=cosπ2⇒θ=π2,π4[∵θ≠nπ,nϵZ]
