Trigonometric Functions Test -8

Result

Trigonometric Functions Test -8

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Question 1
1 / -0

In a triangle ABC, the line joining the circumcentre and the incentre is parallel to BC, then cos B + cos C =

A
3/4

B
1

C
1/2

D
3/2

Solution

Using the given condition we have r = R cos A which gives r/R = cos A.hence Cos A + Cos B + cos C -1 = cos A which gives cos B + cos C = 1.
Question 2
1 / -0

The value of the expression tan 1^o tan 2^o tan 3^o … tan 89^o is equal to

A
0

B
1

C
∞

D
not defined

Solution

Since tan 1 .tan 89 =1...... only tan 45 in the middle which has the value 1. hence the product is 1.
Question 3
1 / -0

If sin 2 θ = cos 3 θ, then θ is equal to (0 ≤ θ ≤ 90^∘)

A
36^o

B
18^o

C
18 or 90^∘

D
none of these

Solution

When the value of θ is replace by 18 both Lhs and Rhs are equal since 38 and 54 are complimentary angles.
Question 4
1 / -0

The maximum value of sinα + sinβ + sinγ , where α, β, γ are positive real numbers satisfying α + β + γ = π is

A
zero

B
(-) 3

C
negative

D
positive

Solution

Since sine ratio is positive in both first and second quadrants and the angles sum up to 180 and the ratios are related to triangle , the value is always positive.