Sin230-4-cot245-sec260-cosec245-sec230-

(sin^230^∘+4 cot^245^∘ sec^260^∘)(cosec^245^∘ sec^230^∘) Putting values of the trigonometric values, (sin^230^∘+4 cot^245^∘ sec^260^∘)(cosec^245^∘ sec^230^∘) = ...

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Standard X

Mathematics

Standard Values of Trigonometric Ratios

sin230∘+4 cot...

Question

$(s i n^{2} 30^{\circ} + 4 c o t^{2} 45^{\circ} - s e c^{2} 60^{\circ}) (c o s e c^{2} 45^{\circ} s e c^{2} 30^{\circ})$

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Solution

$(s i n^{2} 30^{\circ} + 4 c o t^{2} 45^{\circ} - s e c^{2} 60^{\circ}) (c o s e c^{2} 45^{\circ} s e c^{2} 30^{\circ})$

Putting values of the trigonometric values,

$(s i n^{2} 30^{\circ} + 4 c o t^{2} 45^{\circ} - s e c^{2} 60^{\circ}) (c o s e c^{2} 45^{\circ} s e c^{2} 30^{\circ}) = (\frac{1}{4} + 4 \times 1 - 4) (2 \times \frac{4}{3})$

$= \frac{1}{4} \times \frac{8}{3} = \frac{2}{3}$

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Similar questions

Evaluate each of the following

$(c o s e c^{2} 45^{o} s e c^{2} 30^{o}) (s i n^{2} 30^{o} + 4 c o t^{2} 45^{o} - s e c^{2} 60^{o})$

Q. Evaluate each of the following

(cosec² 45° sec² 30°) (sin² 30° + 4 cot² 45° − sec² 60°)

Q. (sin²30° + 4cot²45° − sec²60°) = ?
(a) 0
(b)

\frac{1}{4}

Q. Let S =

{sin}^{2} 30^{\circ} + {sin}^{2} 45^{\circ} + {sin}^{2} 60^{\circ}

and

P =

{cosec}^{2} 45^{\circ} . {sec}^{2} 30^{\circ} . {sin}^{3} 90^{\circ} . cos 60^{\circ}

, then the correct statement is

Q. Evaluate the following :

(c o s e c^{2} 45^{\circ} s e c^{2} 30^{\circ}) (s i n^{2} 30^{\circ} + 4 c o t^{2} 45^{\circ} - s e c^{2} 60^{\circ})

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(sin230∘+4 cot245∘−sec260∘)(cosec245∘ sec230∘)

(sin230∘+4 cot245∘−sec260∘)(cosec245∘ sec230∘) Putting values of the trigonometric values, (sin230∘+4 cot245∘−sec260∘)(cosec245∘ sec230∘)=(14+4×1−4)(2×43) =14×83=23

$(s i n^{2} 30^{\circ} + 4 c o t^{2} 45^{\circ} - s e c^{2} 60^{\circ}) (c o s e c^{2} 45^{\circ} s e c^{2} 30^{\circ})$