Relation between Trigonometric Ratios

Q.

Prove the following trigonometric identities:

$si{n}^{2}Aco{t}^{2}A+co{s}^{2}Ata{n}^{2}A=1$

[1 Mark]
[RD Sharma]
[Trigonometic Ratios]

Q. Simplify $sin\theta \times cosec\theta \times cot\theta .$

1. $tan\theta$
2. $sin\theta$
3. $cot\theta$
4. $sec\theta$

Q. $\text{If}sin\theta =\frac{4}{5}\text{and}cos\theta =\frac{3}{5},\text{then find}tan\theta .$

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

Q. If the value of $sec\theta =\frac{5}{2}$ what is the value of $cos\theta$?

1. $\frac{5}{2}$
2. $\frac{2}{5}$
3. $1$
4. $Cannotsay$

Q.

Simplify the expression:
$\frac{cosec\theta }{cot\theta }$

1. $sin\theta$

2. $sec\theta$

3. $cos\theta$

4. $tan\theta$

Q.

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

1. True

2. False

Q.

If $0^{\circ }<\theta <{90}^{\circ }$, $\sqrt{se{c}^2\theta +cose{c}^2\theta }$ =

1. tan θ + cot θ

2. tan θ - cot θ

3. - tan θ + cot θ

4. - tan θ - cot θ

Q.

Tell whether the given expression is true or false

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

1. False

2. True

Q.

If Sin A +Cosec A= 2, then $si{n}^2$A + $cose{c}^2$A =__

Q.

$\frac{tan\theta }{sec\theta }$ + $\frac{cot\theta }{cosec\theta }$ in terms of $sin\theta$ and $cos\theta$ (if $sin\theta$ = x and $cos\theta$ = y) can be written as:

__