Complementary Trigonometric Ratios

Q. If the value of $tan\alpha =\frac{5}{2}$, then find the value of $cot\theta$.
Given : $\alpha +\theta ={90}^{\circ }.$

1. $\frac{5}{\sqrt{21}}$
2. $5$
3. $\frac{5}{2}$
4. $\frac{\sqrt{21}}{2}$

Q. Which of the following trigonometric ratios will have the same value as cot ${53}^{\circ }$?

1. $sin{65}^{\circ }$
2. $tan{47}^{\circ }$
3. $tan{37}^{\circ }$
4. $cosec{37}^{\circ }$

Q. Which of the following statements hold true for a quadrilateral ABCD?

1. $sin\left(\frac{A+B}{4}\right)=cot\left(\frac{C+D}{4}\right)$
2. $sin\left(\frac{A+B}{4}\right)=cos\left(\frac{C+D}{4}\right)$
3. $tan\left(\frac{A+C}{4}\right)=cot\left(\frac{B+D}{4}\right)$
4. $tan\left(\frac{A+C}{4}\right)=cos\left(\frac{B+D}{4}\right)$

Q. $sin{90}^{\circ }cos{0}^{\circ }+sin{88}^{\circ }cos{2}^{\circ }+sin{86}^{\circ }cos{4}^{\circ }+..............+sin{2}^{\circ }cos{88}^{\circ }+sin{0}^{\circ }cos{90}^{\circ }$

1. 1
2. 44
3. 22
4. 23

Q. If $tan4\theta =cot(\theta -{10}^{\circ })$, where $4\theta$ and$(\theta -{10}^{\circ })$ are acute angles then the value of $\theta$ in degrees is ___.

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. $tan{1}^{\circ }.tan{2}^{\circ }.tan{3}^{\circ }...tan{89}^{\circ }$=_________.

1. 1
2. 0
3. $tan{90}^{\circ }$
4. $\sqrt{3}$

Q. State true or false
$tan{1}^{\circ }.tan{89}^{\circ }=tan{2}^{\circ }.tan{88}^{\circ }$

1. True
2. False

Q.

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

1. True
2. False

Q.

If A and B are acute angles of a right angled triangle and sinA = cosB, then

1. A + B =

2. A - B =

3. A + B =

4. A - B =