Question

If $cose{c}^6\theta -{\cot }^6\theta =a{\cot }^4\theta +b{\cot }^2\theta +c$ then $a+b+c=?$

• A. $0$
• B. $7$
• C. $6$
• D. $1$

Answer 1

The correct option is B $7$

Given, ${\text{cosec}}^6\theta -{\cot }^6\theta$

$=(1+{\cot }^2\theta {)}^3-{\cot }^6\theta$

$={\cot }^6\theta +3{\cot }^4\theta +3{\cot }^2\theta +1-{\cot }^6\theta$

$=3{\cot }^4\theta +3{\cot }^2\theta +1$

$⟹a=3,b=3,c=1$

$⟹a+b+c=3+3+1=7$