Question

prove that cosec A tan A= secA​

Answer 1

tan A + cot A=sec A cosec A

tan A + cot A=sec A cosec ALHS=tan A +cot A

tan A + cot A=sec A cosec ALHS=tan A +cot A =sin A/cos A+ cos A/sin A

tan A + cot A=sec A cosec ALHS=tan A +cot A =sin A/cos A+ cos A/sin A =(sin^2 A+cos^2 A)/cos A sin A

tan A + cot A=sec A cosec ALHS=tan A +cot A =sin A/cos A+ cos A/sin A =(sin^2 A+cos^2 A)/cos A sin A =1/cos A sin A

tan A + cot A=sec A cosec ALHS=tan A +cot A =sin A/cos A+ cos A/sin A =(sin^2 A+cos^2 A)/cos A sin A =1/cos A sin A =sec A cosec A

tan A + cot A=sec A cosec ALHS=tan A +cot A =sin A/cos A+ cos A/sin A =(sin^2 A+cos^2 A)/cos A sin A =1/cos A sin A =sec A cosec A =RHS

Answer 2

Step-by-step explanation:

cosecA = 1/sinA

tanA = sinA/cosA

solving LHS and putting the above values,

1/sinA * sinA/cosA

= 1/cosA

as we know 1/cosA is equals to secA= RHS

hence proved