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Answer:
- Step 1: Take the L.C.M of L.H.S
- STEP 2 :Take 2 as common from numerator
- Step 3 : then cancel out common things from num. & den.
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Step-by-step explanation:
1/2 [ sin x/1+cos x + 1+cos x/sin x ] = 1/sin x
=> 1/2 [ sin x * sin x + (1+cos x)²] / sin x (1 + cos x)
=> 1/2 [ sin²x + 1 + cos²x + 2cosx]/ sin x (1+cos x)
[ sin²x + cos²x = 1 ]
=> 1/2 [ 2 + 2 cos x ] / sin x (1+cos x)
=> 1/2 [ 2(1+cos x) ] / sin x (1+cos x)
=> 1+cos x / sin x ( 1+cos x) [ 1 + cos x cancels out ]
=> 1/sin x => RHS hence proved
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