Question

Prove this question quickly with correct and clear steps pls

Answer 1

Answer:

Good morning mate. For my convenience i am using 'a' instead of theta.

Step-by-step explanation:

1/2 [ sin a / 1+cos a  + 1+cos a/sin a ] = 1 / sin a

now, LHS

1/2 [ sin a / 1+cos a  + 1+cos a/sin a ]

1/2 [ sin² a + (1 + cos a)² /  (1+cos a)(sin a) ]     -    taking lcm

1/2 [ sin²a + cos²a +1 + 2cos a ] / (1+cos a)(sin a) ]    -   using ( a + b )²

1/2 [ 2 + 2 cos a ] / (1+cos a)(sin a) ]   -    [sin²a + cos²a = 1]

1/2 × 2 [1 + cos a / (1+cos a)(sin a) ]     -  taking 2 as common

1 × 1 /sin a = 1/sin a     [ 2 and 1+ cos a  are cancelled ]

hence, LHS = RHS

The trick here is to solve the braces part by taking the LCM.

HOPE YOU GET IT...