cot 2 (π/6)+ operatornamecosec (5 π/6)+3 tan 2 (π/6) is equal to

Question

cot 2 (π/6)+ operatornamecosec (5 π/6)+3 tan 2 (π/6) is equal to (A) 1 (B) 3 (C) 5 (D) None of these

Tardigrade Admin · Accepted Answer

cot 2 (π/6)+ operatornamecosec (5 π/6)+3 tan 2 (π/6) =(√3)2+ operatornamecosec(π-(π/6))+3((1/√3))2 =3+ operatornamecosec (π/6)+3 × (1/3) [∵ operatornamecosec(π-θ)= operatornamecosec θ] =3+2+1=6

Q. $cot^{2} \frac{π}{6} + cosec \frac{5 π}{6} + 3 tan^{2} \frac{π}{6}$ is equal to

1

3

5

None of these

$cot^{2} \frac{π}{6} + cosec \frac{5 π}{6} + 3 tan^{2} \frac{π}{6}$
$= (3)^{2} + cosec (π - \frac{π}{6}) + 3 (\frac{1}{3})^{2}$
$= 3 + cosec \frac{π}{6} + 3 \times \frac{1}{3} [∵ cosec (π - θ) = cosec θ]$
$= 3 + 2 + 1 = 6$

Q. cot26π​+cosec65π​+3tan26π​ is equal to

1

3

5

None of these

cot26π​+cosec65π​+3tan26π​ =(3​)2+cosec(π−6π​)+3(3​1​)2 =3+cosec6π​+3×31​[∵cosec(π−θ)=cosecθ] =3+2+1=6

Q. $cot^{2} \frac{π}{6} + cosec \frac{5 π}{6} + 3 tan^{2} \frac{π}{6}$ is equal to

$cot^{2} \frac{π}{6} + cosec \frac{5 π}{6} + 3 tan^{2} \frac{π}{6}$
$= (3)^{2} + cosec (π - \frac{π}{6}) + 3 (\frac{1}{3})^{2}$
$= 3 + cosec \frac{π}{6} + 3 \times \frac{1}{3} [∵ cosec (π - θ) = cosec θ]$
$= 3 + 2 + 1 = 6$