Question

Prove that tan^2A +cot^2A + 2 = sec^2A x cosec^2A​

Answer 1

sec^2A×cosec^2A.

step by step explanation

GIVEN:

LHS-tan^2A+cot^2A

RHS-sec^2A×cosec^2A

since we know ,

tan^2=sin^2/cos^2 and cot^2=cos^2/sin^2

therefore,sin^2A/cos^2A+cos^2A/sin^2A

equating the denominator we get,

sin^4A+cos^4A/sin^2A×cos^2A=

(sin^2A+cos^2A)^2/cos^2A×sin^2A

since we know ,sin^2+cos^2=1

therefore,(1)^2/cos^2A×cos^2A=

1/cos^2A×1/sin^2A

now we know,

1/cos=sec and 1/sin=cosec

therefore sec^2A×cosec^2A

LHS=RHS

hence proved