Question

Find out the value of $\sqrt{se{c}^2\theta +cose{c}^2\theta }$

• A. $tan\theta +cot\theta$
• B. $sec\theta +cosec\theta$
• C. $\frac{se{c}^2\theta }{cose{c}^2\theta }$
• D. $tan\theta -Sec\theta$

Answer 1

Answer: (A)

$tan\theta +cot\theta$

$\sqrt{se{c}^2\theta +cose{c}^2\theta }$

$=\sqrt{se{c}^2\theta +cose{c}^2\theta +2-2}$

$=\sqrt{se{c}^2\theta -1+cose{c}^2\theta -1+2}$

$=\sqrt{ta{n}^2\theta +co{t}^2\theta +2}$

$=\sqrt{ta{n}^2\theta +co{t}^2\theta +2\times tan\theta \times cot\theta }$

$=\sqrt{(tan\theta +cot\theta {)}^2}$

$=tan\theta +cot\theta$

Hence, option 'A' is correct.