Find the value of sin 50-cos 40-cosec 40- 50-4 cos 50-cosec 40-

Sin50 #176;cos40 #176;+cosec40 #176;sec50 #176; 4cos50 #176; #160;cosec40 #176;=cos90 #176; 50 #176;cos40 #176;+sec90 #176; 40 #176;sec5 ...

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Standard X

Mathematics

Relation between Trigonometric Ratios

Find the valu...

Question

$Find the value of \frac{\sin 50 °}{\cos 40 °} + \frac{cosec 40 °}{\sec 50 °} - 4 \cos 50 ° cosec 40 ° .$

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Solution

$\frac{\sin 50 °}{\cos 40 °} + \frac{cosec 40 °}{\sec 50 °} - 4 \cos 50 ° cosec 40 ° = \frac{\cos (90 ° - 50 °)}{\cos 40 °} + \frac{\sec (90 ° - 40 °)}{\sec 50 °} - 4 \sin (90 ° - 50 °) cosec 40 ° = \frac{\cos 40 °}{\cos 40 °} + \frac{\sec 50 °}{\sec 50 °} - 4 \sin 40 ° \times \frac{1}{\sin 40 °} = 1 + 1 - 4 = - 2$

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Similar questions

Q. 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 ˚

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 sin50°cos40°+cosec40°sec50°-4cos50° cosec40°.

sin50°cos40°+cosec40°sec50°-4cos50° cosec40°=cos90°-50°cos40°+sec90°-40°sec50°-4sin90°-50° cosec40°=cos40°cos40°+sec50°sec50°-4sin40°×1sin40°=1+1-4=-2

$Find the value of \frac{\sin 50 °}{\cos 40 °} + \frac{cosec 40 °}{\sec 50 °} - 4 \cos 50 ° cosec 40 ° .$