Question

Evaluate sin 70/ cos 20 + cosec 36/ sec 54 - 2 cos 43 cosec 47/tan 10 tan 40 tan 50 tan 80

Answer 1

Answer:

Step-by-step explanation:

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 Ans.

Answer 2

Answer:

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