Question
Find the value of sin(θ) if 2sinθ = tanθ, for 0 < θ
< 90°.Solution
We know that tanθ = sinθ/cosθ. Given 2sinθ = tanθ, we have 2sinθ = sinθ/cosθ. Multiplying both sides by cosθ, we get 2sinθ * cosθ = sinθ. Dividing both sides by sinθ, we get 2cosθ = 1. Thus, cosθ = 1/2. Now, sin²θ = 1 - cos²θ = 1 - (1/2)² = 1 - 1/4 = 3/4, so sinθ = √3/2.
Which of the following expressions will be true if the expression ‘V ≥ W < X = Y’ is definitely true?
Statements:
Q ≥ J ≤ V; U > J > X; M = U < P
Conclusions:
I. P > X
II. V ≥ M
Statements: B < W ≥ A ≥ X; N ≤ C < Q = X
Conclusions:
I. Q ≥ W
II. W > C
III. N < AÂ
Statement: D > T > G > C > M; J > C > U
Conclusion:
I. J > M
II. U < D
Which one the following symbols should replace the question mark in the given expression, in order to make the expressions M ≤ J as well as O > L ...
Statement: M<N≥O =A ≥P;P<R;N<T
Conclusions:
I. M < R
II. T > R
Statements: Q < R = S ≥ T = U; S < V; S = X
Conclusion: I. X ≥ U II. V < Q
In the question, assuming the given statements to be true, find which of the conclusion (s) among given three conclusions is/are definitely true and th...
Statements: H ≥ D = R > I < M > U > P ≤ N
Conclusion I: H > R
II: P < M
Statements: E ≥ F ≥ A = M, F ≥ N > W ≥ X
Conclusion:
I. E ≥ X
II. E > X
