If A, B and C are the angles of a triangle and \( \begin{vmatrix} 1 & 1 & 1 \\ 1+\sin A & 1+\sin B & 1+\sin C \\ \sin A+\sin^{2}A & \sin B+\sin^{2}B & \sin C+\sin^{2}C \end{vmatrix} = 0 \), then which one of the following is correct?
A.
The triangle ABC is isosceles
B.
The triangle ABC is equilateral
C.
The triangle ABC is scalene
D.
No conclusion can be drawn with regard to the nature of the triangle
Consider the following in respect of matrices A and B of same order:
1. \( A^{2} - B^{2} = (A + B)(A - B) \)
2. \( (A - I)(I + A) = O \Leftrightarrow A^{2} = I \)
where I is the identity matrix and O is the null matrix.
Which of the above is/are correct?
If \( \sec(\theta - \alpha) \), \( \sec\theta \) and \( \sec(\theta + \alpha) \) are in AP, where \( \cos\alpha \neq 1 \), then what is the value of \( \sin^{2}\theta + \cos\alpha \)?
A balloon is directly above one end of a bridge. The angle of depression of the other end of the bridge from the balloon is \( 48^{\circ} \). If the height of the balloon above the bridge is 122 m, then what is the length of the bridge?
A is an angle in the fourth quadrant. It satisfies the trigonometric equation \( 3(3 - \tan^{2}A - \cot A)^{2} = 1 \). Which one of the following is a value of A?
