Sin 70-cos 20-sin 59-cos 31-8 sin 2 30-

The correct option is D 0 sin 70^∘/cos 20^∘ + sin 59^∘/cos 31^∘ 8 sin^2 30^∘ = sin (90^∘ 20)/cos 20^∘ + sin (90 31^∘)/cos 31 8 (1/2 )^2 (∵ sin nbsp;(90 ...

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Byju's Answer

Standard IX

Mathematics

Variation of Trigonometric Ratios from 0 to 90 Degrees

sin 70∘/cos 2...

Question

$\frac{s i n 70^{\circ}}{c o s 20^{\circ}} + \frac{s i n 59^{\circ}}{c o s 31^{\circ}} - 8 s i n^{2} 30^{\circ} =$ ____

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Solution

The correct option is A
0

$\frac{s i n 70^{\circ}}{c o s 20^{\circ}} + \frac{s i n 59^{\circ}}{c o s 31^{\circ}} - 8 s i n^{2} 30^{\circ}$

$= \frac{s i n (90^{\circ} - 20)}{c o s 20^{\circ}} + \frac{s i n (90 - 31^{\circ})}{c o s 31} - 8 {(\frac{1}{2})}^{2}$

$(∵ s i n (90 - θ) = c o s θ)$

$= \frac{c o s 20^{\circ}}{c o s 20^{\circ}} + \frac{c o s 31^{\circ}}{c o s 31} - 8 (\frac{1}{4})$

= 1 + 1 - 2

= 0

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Similar questions

Q. Find the value of the following:-
(a)

\frac{s i n 31^{\circ}}{2 c o s 59^{\circ}}

(b)

\frac{s e c 70^{\circ}}{2 c o s e c 20^{\circ}} + \frac{s i n 59^{\circ}}{c o s 31^{\circ}}

Q. Evaluate the following :

\frac{c o s 20}{s i n 70}

Q. Evaluate:

cos 20^{\circ} cos 70^{\circ} - sin 20^{\circ} sin 70^{\circ}

sin70/cos20+cosec20/sec70-2cos70cosec20.Simplify

Q. Write the value of

|\begin{matrix} \sin 20 ° & - \cos 20 ° \\ \sin 70 ° & \cos 70 ° \end{matrix}|

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sin 70∘cos 20∘+sin 59∘cos 31∘−8 sin2 30∘=____

The correct option is A 0 sin 70∘cos 20∘+sin 59∘cos 31∘−8 sin2 30∘ =sin (90∘−20)cos 20∘+sin (90−31∘)cos 31−8(12)2 (∵ sin(90−θ)=cos θ) =cos 20∘cos 20∘+cos 31∘cos 31−8(14) = 1 + 1 - 2 = 0

$\frac{s i n 70^{\circ}}{c o s 20^{\circ}} + \frac{s i n 59^{\circ}}{c o s 31^{\circ}} - 8 s i n^{2} 30^{\circ} =$ ____