Question

tan3theta/ 1+tan2theta +cot3theta/1+cot2theta



= sec theta cosectheta- 2 sintheta costheta​

Answer 1

Step-by-step explanation:

tan³A/1+tan²A+cot³A/1+cot²A

tan³A/1+tan²A+cot³A/1+cot²A=tan³A/sec²A+cot³A/cosec²A

tan³A/1+tan²A+cot³A/1+cot²A=tan³A/sec²A+cot³A/cosec²A=sin³A/sinA+cos³A/cosA

tan³A/1+tan²A+cot³A/1+cot²A=tan³A/sec²A+cot³A/cosec²A=sin³A/sinA+cos³A/cosA=sin⁴A+cos⁴A/cosAsinA

tan³A/1+tan²A+cot³A/1+cot²A=tan³A/sec²A+cot³A/cosec²A=sin³A/sinA+cos³A/cosA=sin⁴A+cos⁴A/cosAsinA=(sin²A+cos²A)²-2sin²Acos²A/sinAcosA

tan³A/1+tan²A+cot³A/1+cot²A=tan³A/sec²A+cot³A/cosec²A=sin³A/sinA+cos³A/cosA=sin⁴A+cos⁴A/cosAsinA=(sin²A+cos²A)²-2sin²Acos²A/sinAcosA=1-2sin²Acos²A/sinAcosA

tan³A/1+tan²A+cot³A/1+cot²A=tan³A/sec²A+cot³A/cosec²A=sin³A/sinA+cos³A/cosA=sin⁴A+cos⁴A/cosAsinA=(sin²A+cos²A)²-2sin²Acos²A/sinAcosA=1-2sin²Acos²A/sinAcosA=secAcosecA-2sinAcosA