Complementary Trigonometric Ratios

Q.

How do you find a double angle formula for $\sec 2x$ in terms of only $\mathrm{cosec}x$ and $\sec x$?

Q.

If $A=35°,B=15°$then $C=40°,$then $\tan A\tan B+\tan B\tan C+\tan C\tan A$ is equal to

1. $0$

2. $1$

3. $2$

4. $3$

Q.

Evaluate:

${\cos }^2{25}^{\circ }–{\sin }^2{65}^{\circ }–{\tan }^2{45}^{\circ }$

Q.

Tell whether the given expression is true or false

Cosec A = $\frac{1}{sinA}$

1. True

2. False

Q.

$\tan 51°$ is equal to:

Q.

Evaluate :

$3\cos {80}^{\circ }cosec{10}^{\circ }+2\sin {59}^{\circ }\sec {31}^{\circ }$

Q. $\tan {75}^o+\cot {75}^o=4$.

Q.

If sec 5A = cosec(A - ${30}^{\circ }$) and A is an acute angle, then find the value of A in degrees.

___

Q. $provethat\frac{sinA-2{sin}^{3}A}{2{cos}^{3}A-cosA}=tanA$

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

Q.

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

1. True

2. False

Q. find the value of Tan 49/Cot 41

Q. Show that $\frac{\cos 9^o+\sin 9^o}{\cos 9^o-\sin 9^o}=\cot {36}^o$

Q. If $\frac{x{\text{cosec}}^2{30}^o{\sec }^2{45}^o}{8{\cos }^2{45}^o{\sin }^2{90}^o}={\tan }^2{60}^o-{\tan }^2{45}^o$, then $x$ is :

1. $1$
2. $-1$
3. $2$
4. $0$

Q.

Match column B to column A

$$\begin{array}{cc}ColumnA& ColumnB\\ \left(a\right)sin(90-A)& \left(i\right)cosA\\ \left(b\right)tan(90-A)& \left(ii\right)cosecA\\ \left(c\right)sec(90-A)& \left(iii\right)cotA\end{array}$$

1. (i) – a , (ii) – c , (iii) - b

2. (i) -b, (ii)-c, (iii)-a

3. (i) – a , (ii) – b , (iii) - c

4. (i) – b , (ii) – a , (iii) - c

Q. Find the value of :$\frac{1}{{\sin }^{2}y}-\frac{1}{{\tan }^{2}y}$

Q.

Fill in the blanks
i) $tan{48}^{\circ }.tan{23}^{\circ }.tan{42}^{\circ }.tan{67}^{\circ }$ = ___
ii) $cos{38}^{\circ }.cos{52}^{\circ }-sin{38}^{\circ }.sin{52}^{\circ }$ = ___

Q. If $A$ and $B$ are acute angles and $\sin A=\cos B$, then find the value of $A+B$.

Q. If $\sin 3A=\cos (A-{26}^o)$, where $3A$ is an acute angle, find the value of $A$.

Q. Find the magnitude of angle $A$, if :
$2\sin A\cos A-\cos A-2\sin A+1=0$

Q. Evaluate:
$\left(i\right)\text{Sin}({90}^{\circ }-A)\text{sin A - cos}({90}^{\circ }-A)\text{cosA}$
$\text{(ii)}si{n}^2{35}^{\circ }-co{s}^2{55}^{\circ }$

Q. The value of $\frac{\tan {15}^{\circ }}{\cot {75}^{\circ }}$ is

1. $\cos {90}^{\circ }$
2. $\sin {30}^{\circ }$
3. $\tan {45}^{\circ }$
4. $\text{cosec}{75}^{\circ }$

Q.

Q. Simplify $\cos {38}^{\circ }\cos {52}^{\circ }-\sin {38}^{\circ }\sin {52}^{\circ }$

Q. In a triangle $ABC,$ write $\cos \left(\frac{B+C}{2}\right)$ in terms of angle $A$

Q. Evaluate : $\frac{2}{3}({\cos }^4{30}^o-{\sin }^4{45}^o)-3({\sin }^2{60}^o-{\sec }^2{45}^o)+\frac{1}{4}{\cot }^2{30}^o$

1. $\frac{163}{24}$
2. $\frac{123}{24}$
3. $\frac{113}{24}$
4. $\frac{183}{24}$

Q. Solve
${\cos }^{-1}x=2{\cos }^{-1}\sqrt{\frac{1+x}{2}}$.

Q. Evaluate $co{s}^2\left(67\right)-si{n}^2\left(23\right)$

Q. Without using tables, prove the following $\sin {40}^o-\cos {70}^o=\sqrt{3}\cdot \cos {80}^o$.

Q. If $\sin x+\sin 2x+\sin 3x=2,$ then the value of $x$ is

1. None of these
2. ${45}^0$
3. ${30}^0$
4. ${60}^0$