Question

(3 tan 41 ° / cot 49° ) square - (sin 35 °sec55° / tan 10° tan 20° tan60° tan 70° tan 80°) square

Answer 1

3²-1/√3

=9-1/√3

=9√3-1

=15.50-1= 14.5

Answer 2

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26/3

step-by-step explanation:

Given,

${(3tan 41°/cot 49°)}^{2}$ - ${(sin 35° sec 55°/ tan 10° tan 20° tan 60° tan 70° tan 80°)}^{2}$

We know that,

sin (90°-μ) = cos μ

cosec(90-μ) = sec μ

tan(90°-μ) = cot μ

so,

cot 49° = tan (90-49°) = tan 41°

sec 55° = cosec (90 - 55) = cosec 35°

tan 80° = cot (90-80) = cot 10°

tan 70° = cot(90-70) = cot 20°

Putting all these values ,

we get,

= ${(3tan 41°/tan 41°)}^{2}$ - ${(sin 35° cosec 35°/ tan 10° tan 20° tan 60° cot 20° cot 10°)}^{2}$

now,

we know that,

tan μ cot μ = 1

and,

sin μ cosec μ = 1

and

tan 60° = root 3

so,

according to this,

we get,

= ${(3)}^{2}$ - ${(1/ root3)}^{2}$

= 9 - 1/3

= (27-1)/3

= 26/3