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

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Solution

sin x = cos (90-x)
sin 70 = cos 20

hence , sin 70 / cos 20 = 1

similarly , cosec x = sec (90-x)

cosec 20 = sec 70

hence , cosec 20 / sec 70 = 1

and , cos x = sin (90 - x )

cos 70 = sin 20

and cosec x = 1/ sin x

hence cosec 20 = 1/ sin 20

and so , 2sin 20. cosec20 = 2

hence , sin 70 / sec 20 + cosec 20 / sec 70 - 2cos70 . cosec 20 = 1 + 1 - 2 = 0

hence , answer is 0

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Similar questions

Q. Prove that

\frac{sin 70^{\circ}}{cos 20^{\circ}} + \frac{cosec 20^{\circ}}{sec 70^{\circ}} - 2 cos 70^{\circ} cosec 20^{\circ} = 0

Prove that:

(i) tan $20^{o} t a n 35^{o} t a n 45^{o} t a n 55^{o} t a n 70^{o} = 1$

(ii) sin $48^{o} s e c 42^{o} + c o s 48^{o} c o s e c 42^{o} = 2$

(iii) $\frac{s i n 70^{o}}{c o s 20^{o}} + \frac{c o s e c 20^{o}}{s e c 70^{o}} - 2 c o s 70^{o} c o s e c 20^{o} = 0$

(iv) $\frac{c o s 80^{o}}{s i n 10^{o}} + c o s 59^{o} c o s e c 31^{o} = 2$

Prove that:

(i) $\frac{s i n 70^{\circ}}{c o s 20^{\circ}} + \frac{c o s e c 20^{\circ}}{s e c 70^{\circ}} - 2 c o s 70^{\circ} c o s e c 20^{\circ} = 0$

(ii) $\frac{c o s 80^{\circ}}{s i n 10^{\circ}} + c o s 59^{\circ} c o s e c 31^{\circ} = 2$

(iii) $\frac{2 s i n 68^{\circ}}{c o s 22^{\circ}} - \frac{2 c o t 15^{\circ}}{5 t a n 75^{\circ}} - \frac{3 t a n 45^{\circ} t a n 20^{\circ} t a n 40^{\circ} t a n 50^{\circ} t a n 70^{\circ}}{5} = 1$

(iv) $\frac{s i n 18^{\circ}}{c o s 72^{\circ}} + \sqrt{3} (t a n 10^{\circ} t a n 30^{\circ} t a n 40^{\circ} t a n 50^{\circ} t a n 80^{\circ}) = 2$

(v) $\frac{7 c o s 55^{\circ}}{3 s i n 35^{\circ}} - \frac{4 (c o s 70^{\circ} c o s e c 20^{\circ})}{3 (t a n 5^{\circ} t a n 25^{\circ} t a n 45^{\circ} t a n 65^{\circ} t a n 85^{\circ})} = 1$

9 sec70° sin20° + cosec70° cos20° = ___.

Q. Evaluate the following :

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

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