Cot90o - -sin90o - -sin-cot-40o-tan-50o-cos2-20o-cos2-70o - - a 0 b 1 c -1 d none of these

Cot(90^o θ)sin(90^o θ)/sin θ+cot 40^o/tan 50^o (cos^2 20^o+cos^2 70^o) = tan θ× cos θ/sin θ + cot 40^o/cot(90 50)^o (cos^2 20^o+sin^2(90 70)^o) = sin θ/ co ...

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Byju's Answer

Standard X

Mathematics

Complementary Trigonometric Ratios

cot90o - θsin...

Question

$\frac{c o t (90^{o} - θ) s i n (90^{o} - θ)}{s i n θ} + \frac{c o t 40^{o}}{t a n 50^{o}} - (c o s^{2} 20^{o} + c o s^{2} 70^{o})$ = ?

(a) 0 (b) 1 (c) -1 (d) none of these

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Solution

$\frac{c o t (90^{o} - θ) s i n (90^{o} - θ)}{s i n θ} + \frac{c o t 40^{o}}{t a n 50^{o}} - (c o s^{2} 20^{o} + c o s^{2} 70^{o})$

$= \frac{t a n θ \times c o s θ}{s i n θ} + \frac{c o t 40^{o}}{c o t (90 - 50)^{o}} - (c o s^{2} 20^{o} + s i n^{2} (90 - 70)^{o})$

$= \frac{\frac{s i n θ}{c o s θ} \times c o s θ}{s i n θ} + \frac{c o t 40^{o}}{c o t 40^{o}} - (c o s^{2} 20^{o} + s i n^{2} 20^{o})$

$= 1 + 1 - 1 = 1$

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Similar questions

\frac{\cot (90 ° - θ) \cdot \sin (90 ° - θ)}{sinθ} + \frac{\cot 40 °}{\tan 50 °} - (\cos^{2} 20 ° + \cos^{2} 70 °) = ?

(a) 3
(b) 2
(c) 1
(d) 0

Q. Without using trigonometric tables, evaluate that :

\frac{{sin}^{2} 20^{\circ} + {sin}^{2} 70^{\circ}}{{cos}^{2} 20^{\circ} + {cos}^{2} 70^{\circ}} + \frac{sin (90^{\circ} - θ) sin θ}{tan θ} + \frac{cos (90^{\circ} - θ) cos θ}{cot θ}

\frac{\sin^{2} 40 ° + \sin^{2} 50 °}{\cos^{2} 20 ° + \cos^{2} 70 °} + \tan 10 ° \tan 20 ° \tan 60 ° \tan 70 ° \tan 80 °

Q. Solve

\frac{cos (90 - θ) sec (90 - θ) tan θ}{csc (90 - θ) sin (90 - θ) cot (90 - θ)} + \frac{tan (90 - θ)}{cot θ} = 2

\frac{cot (90 ° - θ) sin (270 ° + θ) cosec (180 ° + θ)}{cos (- θ) sin (90 ° + θ) tan (360 ° - θ)}

is equal to

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cot(90o−θ)sin(90o−θ)sin θ+cot 40otan 50o−(cos2 20o+cos2 70o) = ? (a) 0 (b) 1 (c) -1 (d) none of these

cot(90o−θ)sin(90o−θ)sin θ+cot 40otan 50o−(cos2 20o+cos2 70o) =tanθ×cosθsin θ+cot 40ocot(90−50)o−(cos2 20o+sin2(90−70)o) =sinθcosθ×cosθsin θ+cot 40ocot40o−(cos2 20o+sin2 20o) =1+1−1=1

$\frac{c o t (90^{o} - θ) s i n (90^{o} - θ)}{s i n θ} + \frac{c o t 40^{o}}{t a n 50^{o}} - (c o s^{2} 20^{o} + c o s^{2} 70^{o})$ = ?

(a) 0 (b) 1 (c) -1 (d) none of these