For how many values of α does the expression (sin α + 2)(sin α + 4)(sin α - 2)(sin α - 4) become zero?
No value
Let the expression be equal to 0. (sin α + 2)(sin α + 4)(sin α - 2)(sin α - 4) = 0 This implies that sin α = 2, sin α = 4, sin α = -2, sin α = -4 Since the range of sin α is [-1, 1], there is no value of α for which the expression becomes zero.
If \( p = \frac{1}{\csc\theta + \cot\theta} \) and \( q = \csc\theta \), then what is the value of \( p^2 - 2pq \)?
What is (1 + cot a - cosec a)(1 + tan a + sec a) equal to?
What is sinθ/1 - cotθ + cosθ/1 - tanθ equal to? (θ ≠ π/4)
Consider the following statements:
I. (cscα - secα) is always positive in the first quadrant.
II. (tanα - cotα) is always negative in the first quadrant.
Which of the statements given above is/are correct?
If cot2θ - 3√3cotθ + 6 = 0, where π/6 ≤ θ < π/2, then what is the value of sinθ + cos2θ?
Which of the following equations is/are possible?
I. sin2θ = (x + y)2/4xy, where x, y are positive unequal real quantities.
II. sinθ + cosθ = x + 1/x, where x is a positive real quantity.
Select the correct answer using the code given below:
If m2(sinθ - 1) + n2(sinθ + 1) = 0, where 0 < θ < π/2, then what is (m2 + n2)cosθ - (m2 - n2)cotθ equal to?
If tan θ = sin a - cos a / sin a + cos a, where θ and α are acute angles, then what is √2sinθ equal to?
What is the value of x, where 0 <= x < 30 deg satisfying tan 3x tan 6x = 1 ?
What is the ratio of the greatest to the smallest value of 2 – 2 sin x – sin 2x, 0 ≤ x ≤ (π/2)?
If sinθ = \(\frac{4}{5}\) , Find the value of sin3θ
If x, y are acute angles, where 0 < x + y < 90° and sin(3x - 40°) = cos (3y + 40°), then the value of tan (x + y) is equal to
What is (1 + cot θ - cosec θ)(1 + tan θ + sec θ) equal to?
If \(\sin \theta =\frac{3}{5}\) and \(\cos \theta =\frac{4}{5}\) , then the value of \(\frac{1+\tan \theta}{1-\cot \theta}\) is: