Question

cot2A-Tan2A=Cosec2A-sec2A prove the RHS = LHS​

Answer 1

Answer:

here is your answer

Step-by-step explanation:

cot2A=cos 2A/sin2A

tan2A= sin2A/cos2A

therefore,

cos A/sin2A-sin2A/cos2A

=cos4A-sin4A/sin2Acos2A

we know that,

a4-b4=(a-b)(a+b)(a2+b2)

= (cosA-sinA)(cosA+sinA)(cos2A+sin2A)/sin2Acos2A

= (a-b)(a+b) = a2- b2

= -(cos2A-sin2A) + 1/sin2Acos2A

=2/sin2Acos2A

=1/sin2A× 1/cos 2A

= cosec2A-sec2A

hence proved