Question

plz answer this question

Answer 1

Hello hello !
______________________________________________________________
LHS

sec⁶∅ = (sec²∅)³ 

          = (1+ tan²∅)³

          = 1+tan⁶∅ + 3 x 1 x tan²∅ +3 x 1 x (tan²∅ ) ²

          = 1+tan⁶∅+ 3tan²∅ + 3tan⁴∅

          = 1+tan⁶∅+ 3tan²∅ ( 1+ tan²∅)

          = 1+tan⁶∅+ 3tan²∅ . sec²∅

          Hence LHS = RHS 
____________________________________________________________

Answer 2

LHS = sec^6∅

= { sec²∅}³

we know ,
sec²∅ - tan²∅ = 1
sec²∅ = 1 + tan²∅ use this here,

= { 1 + tan²∅}³

[ use, (a + b)³ =a³ + b³ + 3a²b + 3ab² ]

= 1 + { tan²∅}³ + 3tan²∅.1² + 3(tan²∅)²∅.1

= tan^6∅ + 3tan⁴∅ + 3tan²∅ + 1

= tan^6∅ + 3tan²∅( 1 + tan²∅ ) +1

[ use, ( 1 + tan²∅) = sec²∅ ]

= tan^6∅ + 3tan²∅.sec²∅ + 1 = RHS