Trigonometric Identities

Q. Simplify the expression-
$(cose{c}^2\theta -1)\times (se{c}^2\theta -1)$

1. $1$
2. $0$
3. $co{t}^2\theta$
4. $ta{n}^2\theta$

Q. Prove the following identities, where the angles involved are acute angles for which the expressions is defined.
sec A + tan A = $\sqrt{\left(\frac{1+sinA}{1-sinA}\right)}$

[3 Marks]
[NCERT]
[Trigonometric Identities]

Q. Which of the following is a trigonometric identity?

1. $1+se{c}^2\theta =ta{n}^2\theta$
2. $1+cose{c}^2\theta =co{t}^2\theta$
3. $si{n}^2\theta =1-co{s}^2\theta$
4. $si{n}^2\theta -co{s}^2\theta =1$

Q.

$(cosec\theta +\cot \theta )\times (1-\cos \theta )=$ _____

1. $\cot \theta$

2. $\sec \theta$

3. $\sin \theta$

4. $cosec\theta$

Q. What is the relation between $sin\theta$ and $cos\theta$ for any value of $\theta$?

1. $si{n}^2\theta -co{s}^2\theta =1$
2. $co{s}^2\theta +1=si{n}^2\theta$
3. $si{n}^2\theta +1=co{s}^2\theta$
4. $1-si{n}^2\theta =co{s}^2\theta$

Q.
What is the length of the third side in the above triangle?

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

Q. What is the relation between $sec\theta$ and $tan\theta$ for any value of $\theta$?

1. $ta{n}^2\theta +1=se{c}^2\theta$
2. None of these
3. $ta{n}^2\theta +se{c}^2\theta =1$
4. $se{c}^2\theta +1=ta{n}^2\theta$

Q.

If ($sec\theta$ - $tan\theta$) = $\frac{1}{3}$, the value of ($sec\theta$ + $tan\theta$) is:

Q.

$se{c}^4\theta -se{c}^2\theta$ is equal to

1. $ta{n}^2\theta -ta{n}^4\theta$
2. $ta{n}^4\theta -ta{n}^2\theta$
3. $ta{n}^4\theta +ta{n}^2\theta$
4. $ta{n}^2\theta -ta{n}^4\theta$

Q.

If $pcot\theta$ = $\sqrt{q^2-p^2}$, then the value of $sin\theta$ is ___. ($\theta$ being an acute angle).

1. 0

2. 

3. 

4.