Calculate sin-70-cos-20- - cosec-36-sec-54-2-cos-43-cosec-47-2-1-1-0-

The correct option is D 0 sin 70^∘/cos 20^∘ + cosec 36^∘/sec 54^∘ 2 cos 43^∘ cosec 47^∘ =sin 70^∘/cos (90^∘ 70^∘) + cosec 36^∘/sec (90^∘ 36^∘) 2 cos 43^∘ cose ...

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Question

Calculate $\frac{sin 70^{\circ}}{cos 20^{\circ}} + \frac{cosec 36^{\circ}}{sec 54^{\circ}} - 2 cos 43^{\circ} cosec 47^{\circ}$ .

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Solution

The correct option is D
0

$\frac{sin 70^{\circ}}{cos 20^{\circ}} + \frac{cosec 36^{\circ}}{sec 54^{\circ}} - 2 cos 43^{\circ} cosec 47^{\circ}$

$= \frac{sin 70^{\circ}}{cos (90^{\circ} - 70^{\circ})} + \frac{cosec 36^{\circ}}{sec (90^{\circ} - 36^{\circ})} - 2 cos 43^{\circ} cosec (90^{\circ} - 43^{\circ})$

$= \frac{sin 70^{\circ}}{sin 70^{\circ}} + \frac{cosec 36^{\circ}}{cosec 36^{\circ}} - 2 cos 43^{\circ} sec 43^{\circ}$

$∵ c o s (90^{\circ} - θ) = s i n θ, s e c (90^{\circ} - θ) = c o s e c θ, c o s e c (90^{\circ} - θ) = s e c θ)$

$= 1 + 1 - 2 cos 43^{\circ} sec 43^{\circ}$

$= 1 + 1 - 2 (∵ cos θ sec θ = 1)$

$= 0$

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Similar questions

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