Question

prove that: (sin a - cosec a)^2 + (cos a - sec a)^2 = tan^2a + cot^2a -1 plz solve that identity I will mark as brainlist sure ​

Answer 1

Step-by-step explanation:

sin²a +cosec²a -2sin a cosec a +cos²a+sec²a -2cos a sec a

=sin²a +cosec²a -2 +cos²a+sec²a -2

Reason -> { sin a cosec a=1 }

{ cos a sec a = 1}

= sin²a + cos²a +cosec²a + sec²a -4

= 1 + 1 + cot²a + 1 + tan²a - 4

Reason -> {sin²a +cos²a =1 }

{ cosec²a = 1 + cot²a }

{ sec²a = 1 + tan²a}

= cot²a + tan²a +3 -4

= tan²a + cot²a - 1

Hence proved