Question

Prove that sin70/cos20+cosec20/sec70-2cos70.×cosec20=1

Answer 1

Correct Question

→ sin70°/cos20° + cosec20°/sec70° - 2 cos70°cosec20° = 0

Proof

L.H.S → sin70°/cos20° + cosec20°/sec70° - 2 cos70°cosec20°

L.H.S → cos(90° - 70°)/cos20° + sec(90° - 20°)/sec70° - 2 cos70° 1/sin20°

L.H.S → cos20°/cos20° + sec70°/sec70° - 2cos70°/[cos(90° - 20°)]

L.H.S → 1 + 1 - 2 cos70°/cos70°

L.H.S → 2 - 2(1)

L.H.S → 0 = R.H.S

Hence Proved

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Remember that

• cos(90° - ∅) = sin∅
• sec(90° - ∅) = cosec∅
• cosec∅ = 1/sin∅