System of Measurement of Angles

If $\mathrm{tan\theta }=\frac{\mathrm{x} \sin \mathrm{a}}{1-\mathrm{x} \cos \mathrm{a}}$  and  $\tan \mathrm{a}=\frac{\mathrm{y} \mathrm{sin\theta }}{1-\mathrm{y} \mathrm{cos\theta }}$, then $\frac{\mathrm{x}}{\mathrm{y}}$ equals to ______.

If sin17⁰ $$=\frac { x }{ y }$$, then sec 17⁰ - sin 73⁰ is equal to

If $\frac{\sin \left(x+y\right)}{\sin \left(x-y\right)}=\frac{\mathrm{a}+\mathrm{b}}{\mathrm{a}-\mathrm{b}}$ , then the value of $\frac{\tan x}{\tan y}$ is equal to_____.

Which is not correct?

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

$\mathrm{ABCD}$ is a square. The diagonals $\mathrm{AC} \mathrm{and} \mathrm{BD}$ meet at $\mathrm{O}$ . Let $\mathrm{K}, \mathrm{L}$ be the points on $\mathrm{AB}$ such that $\mathrm{AO} = \mathrm{AK}$, $\mathrm{BO}= \mathrm{BL}$. If $\angle \mathrm{LOK}=\mathrm{\theta }$, then what is the value of $\tan \mathrm{\theta }?$

Two boats leave a place at the same time. One travels $56 \mathrm{km}$ in the direction $\mathrm{N} 40° \mathrm{E}$, while the other travels $48 \mathrm{km}$ in the direction $\mathrm{S} 80° \mathrm{E}$. What is the distance between the boats?

If $\tan \theta =\frac{p}{q}$ then $\frac{p\sin \theta -q\cos \theta }{p\sin \theta +q\cos \theta }$ is equal to-

If $sin\theta +cos\theta =1$ , then $sin\theta cos\theta$  is equal to:

If $0° < i < 90°$, then find the value of $\sin \left(i\right)+\cos \left(i\right)$.

Find the value of ${\cos }^6\mathrm{X}+{\sin }^6\mathrm{X}-1+3{\sin }^2\mathrm{X} {\cos }^2\mathrm{X}$ $=?$

Find the value of ${\left(\tan \theta +\sec \theta \right)}^2$.

The numerical value of $\cot 18°\left(\cot 72°{\cos }^{2}22°+\frac{1}{\tan 72°{\sec }^{2}68°}\right)$  is_____.

If $0^{°}<\theta <{90}^{°}$ , the value of $\sin \theta +\cos \theta$ is ______.

A person observes the angle of elevation of a building as $30°$. The person proceeds toward the building at a speed of $25\left(\sqrt{3}-1\right) \mathrm{meter} \mathrm{per} \mathrm{hour}$. After two hours, he observes the angle of elevation as $45°$. The height of the building (in $\mathrm{m}$) is

If $a=\sin \left(\frac{\pi }{4}\right),b=\cos \left(\frac{\pi }{4}\right),c=-\cos ec\left(\frac{\pi }{4}\right)$ , then the value of $a^3 + b^3 + c^3$ is equal to_____.

If cos α + sec α = $$\sqrt { 3 }$$ , then the value of cos³α + sec³ α is

The shadow of a pole is found $60\mathrm{m}$ increased when the angle of elevation of sun becomes $30°$on the pole of $45°$. The height of the pole is equal to_____.

Find the value of $\sin \frac{41\mathrm{\pi }}{4}$.

If $\cos \theta =\frac{b}{\sqrt{a^2+b^2}}$ then prove that ${\left(\frac{b+\sqrt{a^2+b^2}}{a}\right)}^2=\frac{\sqrt{a^2+b^2}+b}{\sqrt{a^2+b^2}-b}=\frac{1+\cos \theta }{1-\cos \theta }$