Question

Evaluate sin25degree/ cos 65 degree + cosec 34 degree/ sec 56 degree - 2 * cos 43 degree * cos 47 degree / tan 10 degree * tan 40 degree * tan 60 degree * tan 80 degree

Answer 1

Sin70°/cos20°+cosec36°/sec54°-2cos43°cosec47°/tan10°tan40°tan50°tan80°
=sin70°/cos{(90°×1)-70°}+cosec36°/sec{(90°×1)-36°}-
2cos43°cosec{(90°×1)-43°}/tan10°tan40°tan{(90°×1)-40°}tan{(90°×1)-10°}
=sin70°/sin70°+cosec36°/cosec36°-2cos43°sec43°/tan10°tan40°cot40°cot10°
=1+1-2cos43°(1/cos43°)/tan10°tan40°(1/tan40°)(1/tan10°)
=1+1-2×1/1
=0