Complementary Trigonometric ratios

Q.

If sec 5A° = cosec (A-30)°, then the value of A is ___.

Q. Evaluate :
$cosec{31}^{\circ }-sec{59}^{\circ }$___

Q.

The equation sin($\theta +\Pi$) = -sin $\theta$ for all $\theta$

1. True

2. False

Q. In $△ABC$, $sin\left(\frac{A+B}{2}\right)$ is equal to

1. $Sin\left(\frac{C}{2}\right)$
2. $Cos\left(\frac{C}{2}\right)$
3. $Cot\left(\frac{C}{2}\right)$
4. $Tan\left(\frac{C}{2}\right)$

Q.

Find the measurement of unknown angles in the following figures.

Complement of$77°=d$. Find $d.$

Q.

Evaluate :
$\frac{tan{26}^{\circ }}{cot{64}^{\circ }}$___

Q. If the above statement is true then mention answer as 1, else mention 0 .

Q. If $A={30}^0$, then
$\cos 2A={\cos }^{4}A-{\sin }^{4}A$

Q. Evaluate
$\frac{\sin {36}^{\circ }}{\cos {54}^{\circ }}$

Q. $\tan 9^{\circ }\times \tan {27}^{\circ }\times \tan {63}^{\circ }\times \tan {81}^{\circ }$ is equal to

1. $4$
2. $3$
3. $2$
4. $1$

Q. If $A={45}^{\circ }$, verify that:
$\sin 2A=2\sin A\cos A$

Q. Find the value of ${\sin }^2{18}^0-{\cos }^2{72}^0$

Q. The value of $\sin {60}^0=2\sin {30}^0\cos {30}^0$

Q. If $\sin {50}^o=0.766$, the value of $\sec {40}^{\circ }$ is

1. $1$
2. $.766$
3. $\frac{1}{.766}$
4. $0$

Q. $\tan {48}^{\circ }.\tan {23}^{\circ }.\tan {42}^{\circ }.\tan {67}^{\circ }$ = ___

Q. If $A={30}^0$, then

Q. State true or false.
In $△ABC$, $sin\left(\frac{A+B}{2}\right)=cos\left(\frac{C}{2}\right)$

1. True
2. False

Q. If sec 2A = cosec $(A-{42}^o)$, where 2A is an acute angle, find the value of A.
(2 Marks)

Q.

If $\theta$ is in the first quadrant, then $\sqrt{(1-sin2\theta )}$ = - cos$\theta$

1. True

2. False

Q.

9 cosec70° cos20° - 7 sec70° sin20° = ___.

1. 9

2. 8

3. 7

4. 2

Q.

Match the following:

$\begin{array}{cc}1.sin({90}^{\circ }-A)& a)cosecA\\ 2.tan({90}^{\circ }-A)& b)cotA\\ 3.sec({90}^{\circ }-A)& c)cosA\end{array}$

1. 1- c; 2 - b; 3 - a

2. 1 - a; 2 - b; 3 - c

3. 1 - a; 2 - c; 3 - b

4. 1 - b; 2 - c;3 - a

Q.

What is the value of (sin 18°)/(cos 72°)?

1. 1

2. -1

3. 1/2

4. 0

Q.

$cot\theta$ can also be written as $tan({90}^{\circ }+\theta )$.

1. True

2. False

Q. What is the value of cosec A, if sin A = cos A?

1. √2
2. 0.5
3. 1
4. 2√2