Circular measure, definitions of trigonometric ratio, simple problems on height and distance

If cot θ = 7/8 ; value of (1 + sin θ)(1 - sin θ) / (1 + cos θ)(1 - cos θ) is

An observer, 1.5 meter tall is 28.5 meter away from a chimney. The angle of elevation of the top of the chimney from his eyes is 45°. Height of the chimney is

If 3 sin θ = 4 cos θ, then the value of sec θ is

The ratio of the height and shadow of a tower is √3 : 1. Then the angle of elevation from the end point of the shadow top of the tower is (shadow is to be considered at bottom level of the tower)

In a right-angled triangle PQR, right angled at Q, if tan P = 1, then the value of 2 sin P cos P is

A 15-meter long ladder reached a window, x meter high from the ground when placed against a wall at a distance of y meter. If the angle between ladder and ground is $30^\circ$, then about x and y which of the following is true?

In a right angled triangle $\Delta$ ABC, $\angle$ $B = 90^\circ$ and $\sin$ $A = 5/\sqrt{29}.$ Then which of the following is not true?

In a right angled triangle ABC, right angle is at B. If cot A = 1, then which of the following option is false ?

A tower stands vertically on the ground. From a point on the ground, which is 17 m away from foot of the tower, the angle of elevation of the top of the tower is found to be 30°. What is the height of the tower ?

If $\sec 4\alpha = \csc (\alpha - 20^\circ)$, where $4\alpha$ is an acute angle, then value of $\alpha$ is equal to

If $\sin\theta = \frac{1}{2}$ (where $\t$theta < 90^\circ)$, then $4\cos^3\t$theta - 3\cos\theta$ is :

If in a triangle ABC, angle $ABC = \frac{\pi}{2}$ and sides AB=12 and BC = 5, then the value of sinC + cosA is: