(i) cot 54°/tan 36° + tan 20°/cot 70° – 2 = 0
(ii) sin 50°/cos 40° + cosec 40°/sec 50° – 4 cos 50° cosec 40° + 2 = 0.
Answer :
(i) cot 54°/tan 36° + tan 20°/cot 70° – 2 = 0
LHS = cot 54°/tan 36° + tan 20°/cot 70° – 2
= cot 54°/tan (90° – 54°) + tan 20°/cot (90° – 20°) – 2
= cot 54°/ cot 54° + tan 20°/ tan 20° – 2
= 1 + 1 – 2
= 0
= RHS
(ii) sin 50°/cos 40° + cosec 40°/sec 50° – 4 cos 50° cosec 40° + 2 = 0
LHS = sin 50°/cos 40° + cosec 40°/sec 50° – 4 cos 50° cosec 40° + 2
= sin 50°/cos (90° – 50°) + cosec 40°/sec (90° – 40°) – 4 cos 50° cosec (90° – 50°) + 2
= sin 50°/sin 50° + cosec 40°/cosec 40° – cos 50° sec 50° + 2
= 1 + 1 – (4 cos50°/cos 50°) + 2
= 1 + 1 – 4 + 2
= 4 – 4
= 0
= RHS
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