If $$\tan B = \frac{5}{3}$$, what is the value of $$\frac{\cosec B + \sin B}{\cos B - \sec B}$$?

correct answer:-**1**

If $$6 \tan A \left(\tan A - 1\right) = 5 - \tan A$$, Given that O < A < $$\frac{\pi}{2}$$. what is the value of $$\left(\sin A + \cos A\right)$$?

correct answer:-**2**

A ladder leaning against a wall makes an angle $$\theta$$ with the horizontal ground such that $$\tan \theta = \frac{12}{5}.$$ If the height of the top of the ladder from the wall is 24 m, then what is the distance (in m) of the foot of the ladder from the wall?

correct answer:-**4**

$$\frac{\sin^2 52^\circ + 2 + \sin^{2} 38^\circ}{4 \cos^{2} 43^\circ - 5 + 4 \cos^{2} 47^\circ}$$ is:

correct answer:-**4**

ladder is resting against a wall. The angle between the foot of the ladder and wall is $$60^\circ$$, and the foot of the ladder is 3.6 m away from the wall. The length of the ladder (in m) is:

correct answer:-**4**

If $$4(cosec^2 57 - \tan^2 33) - \cos 90 + y * \tan^2 66 * \tan^2 24 = \frac{y}{2}$$, then the value of y is:

correct answer:-**4**

Let A and B be two towers with the same base. From the mid point of the line joining their feet, the angles of elevation of the tops of A and B are $$30^\circ$$ and $$45^\circ$$, respectively. The ratio of the heights of A and B is :

correct answer:-**2**

If $$4 \theta$$ is an acute angle , and $$\cot 4 \theta = \tan(\theta - 5^\circ)$$ is an acute angle, and $$\cot 46 = \tan(6 - 5^\circ)$$, then what is the value of $$\theta$$?

correct answer:-**1**

If $$4 - 2 \sin^2 \theta - 5 \cos \theta = 0, 0^\circ < \theta < 90^\circ$$, then the value of $$\cos \theta - \tan \theta$$ is:

correct answer:-**4**

Solve for $$ \theta: \cos^{2} - \sin^{2} \theta = \frac{1}{2}, 0 < \theta < 90^\circ$$.

correct answer:-**3**

If $$\cot \theta = \frac{1}{\sqrt{3}}, 0^\circ < \theta^\circ < 90^\circ$$ then the value of $$\frac{2 - \sin^{2} \theta}{1 - \cos^{2} \theta} + (\cosec^{2} \theta - \sec \theta)$$ is:

correct answer:-**4**

A person was standing on a road near a mall. He was 1215 m away from the mall and able to see the top of the mall from the road in such a way that the top of a tree, which is in between him and the mall, was exactly in line of sight with the top of the mall. The tree height is 20 m and it is 60 m away from him. How tall (in m) is the mall?

correct answer:-**3**

Let A and B be two towers with same base. From the midpoint of the line joining their feet. the angles of elevation of the tops of A and B are $$30^\circ$$ and $$60^\circ$$, respectively. The ratio of the heights of B and A is:

correct answer:-**2**

What is the average of sixty terms given below?

$$\cos^{2}x$$, $$\cos^{2}2x \cos^{2}3x$$,... $$\cos^{2}30x$$, $$\sin^{2}x$$, $$\sin^{2}2x$$, $$\sin^{2}3x$$,... $$ \sin^{2}30x$$

correct answer:-**2**

If $$3 \sin^2 \theta - \cos \theta - 1 = 0, 0^\circ < \theta < 90^\circ$$, then what is the value of $$\cot \theta + \cosec \theta ?$$

correct answer:-**3**

If $$\sin A = \frac{1}{2}, A$$ is an acute angle, then find the value of $$\frac{\tan A - \cot A}{\sqrt{3}(1 + \cosec A)}$$

correct answer:-**3**

If $$\frac{\cos^2 \theta}{\cot^2 \theta + \sin^2 \theta - 1} = 3, 0^\circ < \theta < 90^\circ$$, then the value of $$(\tan \theta + \cosec \theta)$$ is:

correct answer:-**1**

$$1 + 2 \tan^2 \theta + 2 \sin \theta \sec^2 \theta, 0^\circ < \theta < 90^\circ$$, is equal to:

correct answer:-**4**

If $$\frac{\sin^2 \theta}{\tan^2 \theta - \sin^2 \theta} = 5, \theta$$ is an acute angle, then the value of $$\frac{24\sin^2\theta-15\sec^2\theta}{6\operatorname{cosec}^2\theta-7\cot^2\theta}$$ is:

correct answer:-**3**

If $$\frac{\sin\theta+\cos\theta}{\sin\theta-\cos\theta}=5$$, then the value of $$\frac{4\sin^2\theta+3}{2\cos^2\theta+2}$$ is:

correct answer:-**2**

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