Question

answer tan+1/tan=sec×cosec

Answer 1

I used 1+tan^2=sec^2

Answer 2

$\mathcal\red{Question:-}$

prove that

tan∅ + 1/tan∅= sec∅cosec∅

$\mathcal\red{Solution:-}$

we have,

LHS

= tan∅ + 1/tan∅

= sin∅/cos∅ + 1/(sin∅/cos∅)

{ °.° tan∅ = sin∅/cos∅ }

= sin∅/cos∅ + cos∅+sin∅

= sin^2∅+cos^2∅/cos∅sin∅

= 1/cos∅ × 1/sin∅

{ °.° sin^2∅ + cos^2∅ = 1 }

= sec∅cosec∅

{ °.° 1/cos∅ = sec∅ , 1/sin∅ = cosec∅}

= RHS

Hence proved

$\bold\red{Thank\:You}$❤