Question

prove that (1+tan² ©)+(1+1/tan²©)=1/sin²©-sin⁴©​

Answer 1

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

☃ ƛƝƧƜЄƦ ☃

Hey !!

$LHS = ( 1 + 1/tan² A ) + ( 1 + 1/Cot²A )$

$= ( 1 + Cot²A ) ( 1 + Tan²A )$

$=> Cosec²A × Sec²A$

$=> 1/Sin²A × 1/Cos²A$

$=> 1/Sin²A Cos²A$

$=> 1/Sin²A ( 1 - Sin²A )$

$=> 1/ Sin²A - Sin⁴A ) = RHS$

$Hence,$

$LHS = RHS = 1/ Sin² A - Sin⁴A .$

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

Answer 2

Hey !!

refer attachment

Hence,Hence,Hence,

━━━━━━━━━━━━━━━━━━━━━━━━