Question

$co{t}^4\theta -ta{n}^4\theta$=?

• A. $2se{c}^2\theta -se{c}^4\theta -2cose{c}^2\theta +cose{c}^4\theta$
• B. $2se{c}^2\theta -se{c}^4\theta$
• C. $2cose{c}^2\theta +cose{c}^4\theta$
• D. none of the above

Answer 1

The correct option is A

$2se{c}^2\theta -se{c}^4\theta -2cose{c}^2\theta +cose{c}^4\theta$

$co{t}^4\theta -ta{n}^4\theta =(co{t}^2\theta {)}^2-(ta{n}^2\theta {)}^2=(cose{c}^2\theta -1{)}^2-(se{c}^2\theta -1{)}^2=cose{c}^4\theta +1-2cose{c}^2\theta -(se{c}^4\theta +1-2se{c}^2\theta )=cose{c}^4\theta +1-2cose{c}^2\theta -se{c}^4\theta -1+2se{c}^2\theta =2se{c}^2\theta -se{c}^4\theta -2cose{c}^2\theta +cose{c}^4\theta$