\left. \begin{array} { l } { ( i ) \operatorname { sin } ^ { 4 } \thet

1.	\left. \begin{array} { l } { ( i ) \operatorname { sin } ^ { 4 } \theta - \operatorname { cos } ^ { 4 } \theta = \operatorname { sin } ^ { 2 } \theta - \operatorname { cos } ^ { 2 } \theta } \\ { \operatorname { tan } ^ { 4 } \theta + \operatorname { tan } ^ { 2 } \theta = \operatorname { sec } ^ { 4 } \theta - \operatorname { sec } ^ { 2 } \theta } \end{array} \right.
Answer» 1) sin²∅+cos²∅ = 1 so, sin⁴∅-cos⁴∅ = (sin²∅+cos²∅)(sin²∅-cos²∅) = 1(sin²∅-cos²∅) 2) sec²∅-tan²∅ = 1 tan⁴∅+tan²∅ =sec⁴∅-sec²∅=> sec⁴∅-tan⁴∅= tan²∅+sec²∅=> (sec²∅-tan²∅)(sec²∅+tan²∅)= tan²∅+sec²∅=> 1(sec²∅+tan²∅) = tan²∅+sec²∅

\left. \begin{array} { l } { ( i ) \operatorname { sin } ^ { 4 } \theta - \operatorname { cos } ^ { 4 } \theta = \operatorname { sin } ^ { 2 } \theta - \operatorname { cos } ^ { 2 } \theta } \\ { \operatorname { tan } ^ { 4 } \theta + \operatorname { tan } ^ { 2 } \theta = \operatorname { sec } ^ { 4 } \theta - \operatorname { sec } ^ { 2 } \theta } \end{array} \right.

Answer»

1) sin²∅+cos²∅ = 1

so, sin⁴∅-cos⁴∅ = (sin²∅+cos²∅)(sin²∅-cos²∅) = 1*(sin²∅-cos²∅)

2) sec²∅-tan²∅ = 1

tan⁴∅+tan²∅ =sec⁴∅-sec²∅=> sec⁴∅-tan⁴∅= tan²∅+sec²∅=> (sec²∅-tan²∅)(sec²∅+tan²∅)= tan²∅+sec²∅=> 1*(sec²∅+tan²∅) = tan²∅+sec²∅