Value of Standard Angle(30,60,90)

Q. The value of $tan{60}^{\circ }cose{c}^2{45}^{\circ }+se{c}^2{60}^{\circ }tan{45}^{\circ }$ is

1. $4+2\sqrt{3}$
2. $4-2\sqrt{3}$
3. $1$
4. $-1$

Q. $△PQR$ is a right-angled triangle at Q. If P = 30° and PQ = 8 cm, find the perimeter of the triangle.

1. $8(\sqrt{3}+2)$ cm
2. $8(\sqrt{2}+1)$ cm
3. $8(\sqrt{3}+1)$ cm
4. $8(\sqrt{3}+3)$ cm

Q. If the value of $2\sin 2\theta =\sqrt{3}$, then find the value of $\theta$.

Q. If $cos$ (A+B) = $\frac{1}{\sqrt{2}}$, then value of A+B is

1. ${45}^{\circ }$
2. ${60}^{\circ }$
3. ${30}^{\circ }$
4. ${90}^{\circ }$

Q. Angle $\left(\theta \right)$ at which $sin\theta \text{and}tan\theta$ are equal is

1. \N

Q.

In any $\Delta ABC$ where $\angle B={90}^{\circ }$, ${\sin }^{2}A+{\cos }^{2}C=1$

1. True

2. False

Q. If $\tan \theta =4$, then $\left(\frac{\tan \theta }{\frac{{\sin }^3\theta }{\cos \theta }+\sin \theta \cos \theta }\right)$ is equal to:

1. $0$
2. $2\sqrt{2}$
3. $\sqrt{2}$
4. $1$

Q. $\frac{2\tan {30}^{\circ }}{1+{\tan }^2{30}^{\circ }}=$

1. $\sin {60}^{\circ }$
2. $\cos {60}^{\circ }$
3. $\tan {60}^{\circ }$
4. $\sin {30}^{\circ }$

Q. In a $\Delta ABC$, if ${\sin }^{2}A+{\sin }^{2}B+{\sin }^{2}C=2$, then the triangle can be

1. equilateral
2. right angled
3. Isosceles
4. None of these

Q. In a $\Delta ABC,$ if $\angle C={90}^{\circ },$ prove that ${\sin }^{2}A+{\sin }^{2}B=1$

Q. Draw the right triangle $ABC$ if angle $A$ is $30$, and the hypotenuse is $2$ m. Find the longest and shortest side.

Q.

Calculate $\frac{\text{sin}{70}^{\circ }}{\text{cos}{20}^{\circ }}+\frac{\text{cosec}{36}^{\circ }}{\text{sec}{54}^{\circ }}-2\text{cos}{43}^{\circ }\text{cosec}{47}^{\circ }$.

Q. If the value of $2\sin 2\theta =\sqrt{3}$, then find the value of $\theta$.