Find the value of the sin 50-cos 40- - cosec 40- 50- - 4 cos 50-cosec 40- - 2sin45-cos45-

sin 50^∘cos 40^∘ + cosec 40^∘ 50^∘ 4 cos 50^∘. cosec 40^∘ +2sin45 #730;cos45 #730; =sin (90 40)^∘cos 40^∘ + cosec (90 50)^∘ 50^∘ 4 cos ( ...

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Byju's Answer

Standard XII

Mathematics

Tangent, Cotangent, Secant, Cosecant in Terms of Sine and Cosine

Find the valu...

Question

Find the value of the $\frac{sin 50^{\circ}}{cos 40^{\circ}} + \frac{cosec 40^{\circ}}{sec 50^{\circ}} - 4 cos 50^{\circ} \cdot cosec 40^{\circ} + 2 sin 45 ˚ cos 45 ˚$ .

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Solution

$\frac{sin 50^{\circ}}{cos 40^{\circ}} + \frac{cosec 40^{\circ}}{sec 50^{\circ}} - 4 cos 50^{\circ} . cosec 40^{\circ} + 2 sin 45 ˚ cos 45 ˚$

$= \frac{sin (90 - 40)^{\circ}}{cos 40^{\circ}} + \frac{cosec (90 - 50)^{\circ}}{sec 50^{\circ}} - 4 cos (90 - 40)^{\circ} . cosec 40^{\circ} + 2 \frac{1}{\sqrt{2}} \frac{1}{\sqrt{2}}$

$= \frac{cos 40^{\circ}}{cos 40^{\circ}} + \frac{sec 50^{\circ}}{sec 50^{\circ}} - 4 sin 40^{\circ} . cosec 40^{\circ} + 1$

$= 1 + 1 - 4 + 1 = - 1$

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Similar questions

Find the value of $\frac{s i n 50^{o}}{c o s 40^{o}} + \frac{c o s e c 40^{o}}{s e c 50^{o}} - 4$ cos $50^{o}$ cosec $40^{o}$ .

Q. Find the value of the following.
(i)

\frac{\sin 50 °}{\cos 40 °} + \frac{\cos e c 40 °}{s e c 50 °} - 4 \cos 50 ° . \cos e c 40 °

Q. Evaluate :

\frac{sin 50^{\circ}}{cos 40^{\circ}} + \frac{c o s e c 40^{\circ}}{sec 50^{\circ}} - 4 cos 50^{\circ} c o s e c 40^{\circ}

Q. Evaluate sin 50°÷cos 40°+cosec40°÷sec50°- 4cos52°.cosec38°

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

(ii) $4 (s i n^{4} 30^{o} + c o s^{4} 60^{o}) - \frac{2}{3} (s i n^{2} 60^{o} - c o s^{2} 45^{o}) + \frac{1}{2} t a n^{2} 60^{o}$

(iii) $\frac{s i n 50^{o}}{c o s 40^{o}} + \frac{c o s e c 40^{o}}{s e c 50^{o}} - 4 c o s 50^{o} c o s e c 40^{o}$

(iv) $t a n 35^{o} t a n 40^{o} t a n 45^{o} t a n 50^{o} t a n 55^{o}$

(v) $c o s e c (65^{o} + θ) - s e c (25^{o} - θ) - t a n (55^{o} - θ) + c o t (35^{o} + θ)$

(vi) $t a n 7^{o} t a n 23^{o} t a n 60^{o} t a n 67^{o} t a n 83^{o}$

(vii) $\frac{2 s i n 68^{o}}{c o s 22^{o}} - \frac{2 c o t 15^{o}}{5 t a n 75^{o}} - \frac{3 t a n 45^{o} t a n 20^{o} t a n 40^{o} t a n 50^{o} t a n 70^{o}}{5}$
(viii) $\frac{3 c o s 55^{o}}{7 s i n 35^{o}} - \frac{4 (c o s 70^{o} c o s e c 20^{o})}{7 (t a n 5^{o} t a n 25^{o} t a n 45^{o} t a n 65^{o} t a n 85^{o})}$
(ix) $\frac{s i n 18^{o}}{c o s 72^{o}} + \sqrt{3} {t a n 10^{o} t a n 30^{o} t a n 40^{o} t a n 50^{o} t a n 80^{o}}$
(x) $\frac{c o s 58^{o}}{s i n 32^{o}} + \frac{s i n 22^{o}}{c o s 68^{o}} - \frac{c o s 38^{o} c o s e c 52^{o}}{t a n 18^{o} t a n 35^{o} t a n 60^{o} t a n 72^{o} t a n 55^{o}}$

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Find the value of the sin50∘cos40∘+cosec 40∘sec50∘−4cos50∘⋅cosec 40∘+2sin45˚cos45˚.

sin50∘cos40∘+cosec 40∘sec50∘−4cos50∘.cosec 40∘+2sin45˚cos45˚=sin(90−40)∘cos40∘+cosec (90−50)∘sec50∘−4cos(90−40)∘.cosec 40∘+21√21√2=cos40∘cos40∘+sec50∘sec50∘−4sin40∘.cosec 40∘+1=1+1−4+1=−1

Find the value of the $\frac{sin 50^{\circ}}{cos 40^{\circ}} + \frac{cosec 40^{\circ}}{sec 50^{\circ}} - 4 cos 50^{\circ} \cdot cosec 40^{\circ} + 2 sin 45 ˚ cos 45 ˚$ .