Evaluate- 229-cos 661-2 8- 17- 45- 73- 82-

Sec 29^∘/cosec 61^∘ + 2 cot8^∘ cot17^∘ cot45^∘ cot73^∘ cot82^∘ = sec29^∘/cosec(90^∘ 29^∘) + + 2 cot8^∘ cot17^∘ (1) cot(90^∘ 17^∘) cot(90^∘ 8^∘) = sec2 ...

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Byju's Answer

Standard X

Mathematics

Range of Trigonometric Ratios from 0 to 90 Degrees

Evaluate: 229...

Question

Evaluate: $\frac{s e c 29^{\circ}}{c o s e c 61^{\circ}}$ + $2 c o t 8^{\circ} c o t 17^{\circ} c o t 45^{\circ} c o t 73^{\circ} c o t 82^{\circ}$

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Solution

$\frac{s e c 29^{\circ}}{c o s e c 61^{\circ}}$ + $2 c o t 8^{\circ} c o t 17^{\circ} c o t 45^{\circ} c o t 73^{\circ} c o t 82^{\circ}$

= $\frac{s e c 29^{\circ}}{c o s e c (90^{\circ} - 29^{\circ})}$ + + $2 c o t 8^{\circ} c o t 17^{\circ} (1) c o t (90^{\circ} - 17^{\circ}) c o t (90^{\circ} - 8^{\circ})$

= $\frac{s e c 29^{\circ}}{s e c 29^{\circ}}$ + $2 c o t 8^{\circ} c o t 17^{\circ} t a n 17^{\circ} t a n 8^{\circ}$

= $1 + 2 c o t 8^{\circ} c o t 17^{\circ} . \frac{1}{c o t 17^{\circ}} . \frac{1}{c o t 8^{\circ}}$ ....

= 1+2 $(∵ tan θ = \frac{1}{cot θ})$

= 3

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Similar questions

Q. Evaluate:

\frac{{sec 29}^{\circ}}{cosec 61^{\circ}} + 2 cot 8^{\circ} cot 17^{\circ} cot 45^{\circ}

cot 73^{\circ} cot 82^{\circ} - 3 (sin^{2} 38^{\circ} + sin^{2} 52^{\circ})

Evalute : $\frac{s e c 29^{\circ}}{c o s e c 61^{\circ}}$ + 2 cot $8^{\circ}$ cot $17^{\circ}$ cot $45^{\circ}$ cot $73^{\circ}$ cot $82^{\circ}$ .

Find the value of $\frac{s e c 29^{\circ}}{c o s e c 61^{\circ}}$ + $2 c o t 8^{\circ} c o t 17^{\circ} c o t 45^{\circ} c o t 73^{\circ} c o t 82^{\circ}$ .

Find the value of: $\frac{s e c 29^{\circ}}{c o s e c 61^{\circ}}$ + $2 c o t 8^{\circ} c o t 17^{\circ} c o t 45^{\circ} c o t 73^{\circ} c o t 82^{\circ}$ .

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Find the value of:
$\frac{s e c 29^{\circ}}{c o s e c 61^{\circ}}$ + $2 c o t 8^{\circ} c o t 17^{\circ} c o t 45^{\circ} c o t 73^{\circ} c o t 82^{\circ}$ .

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Evaluate: sec29∘cosec61∘ + 2cot8∘cot17∘cot45∘cot73∘cot82∘

sec 29∘cosec 61∘ + 2cot8∘ cot17∘ cot45∘ cot73∘ cot82∘ = sec29∘cosec(90∘−29∘) + + 2cot8∘ cot17∘(1) cot(90∘−17∘) cot(90∘−8∘) = sec29∘sec29∘ + 2cot8∘ cot17∘ tan17∘ tan8∘ = 1+2cot8∘cot17∘.1cot17∘.1cot8∘ .... = 1+2 (∵tanθ=1cotθ) = 3

Evaluate: $\frac{s e c 29^{\circ}}{c o s e c 61^{\circ}}$ + $2 c o t 8^{\circ} c o t 17^{\circ} c o t 45^{\circ} c o t 73^{\circ} c o t 82^{\circ}$