I 2-3cos4-30o-sin4-45o-3sin2-60o-sec2-45o-1-4cot2-30o ii 4sin4-30o-cos4-60o-2-3sin2-60o-cos2-45o-1-2tan2-60o iii sin-50o-cos-40o-cosec-40o-sec-50o-4-cos-50o-cosec-40o iv tan-35o-tan-40o-tan-45o-tan-50o-tan-55o v cosec65o-sec25o-tan55o-cot35o- vi tan-7o-tan-23o-tan-60o-tan-67o-tan-83o vii 2-sin-68o-cos-22o-2-cot-15o-5-tan-75o-3-tan-45o-tan-20o-tan-40o-tan-50o-tan-70o-5 viii3-cos-55o-7-sin-35o-4cos-70o-cosec-20o-7tan-5o-tan-25o-tan-45o-tan-65o-tan-85o ix sin-18o-cos-72o-3 tan-10o-tan-30o-tan-40o-tan-50o-tan-80o x cos-58o-sin-32o-sin-22o-cos-68o-cos-38o-cosec-52o-tan-18o-tan-35o-tan-60o-tan-72o-tan-55o

(i) 113/24 (ii) 11/6 (iii) 2 (iv) 1 (v) 0 (vi) √(3) (vii) 1 (viii) 1/7 (ix) 2 (x) 6 √(3)/3 ...

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Byju's Answer

Standard X

Mathematics

Trigonometric Identities

i 2/3cos4 30o...

Question

(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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Solution

(i) $\frac{113}{24}$

(ii) $\frac{11}{6}$

(iii) -2

(iv) 1

(v) 0

(vi) $\sqrt{3}$

(vii) 1

(viii) - $\frac{1}{7}$

(ix) 2

(x) $\frac{6 - \sqrt{3}}{3}$

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Similar questions

Q. Evaluate :

(i)

\frac{2}{3} (\cos^{4} 30 - \sin^{4} 45 °) - 3 (\sin^{2} 60 ° - \sec^{2} 45 °) + \frac{1}{4} \cot^{2} 30 °

(ii)

4 (\sin^{4} 30 ° + \cos^{4} 60 °) - \frac{2}{3} (\sin^{2} 60 ° - \cos^{2} 45 °) + \frac{1}{2} \tan^{2} 60 °

(iii)

\frac{\sin 50 °}{\cos 40 °} + \frac{cosec 40 °}{\sec 50 °} - 4 \cos 50 ° cosec 40 °

(iv) tan 35° tan 40° tan 45° tan 50° tan 55°
(v) cosec (65° + θ) − sec (25° − θ) − tan (55° − θ) + cot (35° + θ)
(vi) tan 7° tan 23° tan 60° tan 67° tan 83°
(vii)

\frac{2 \sin 68 °}{\cos 22 °} - \frac{2 \cot 15 °}{5 \tan 75 °} - \frac{3 \tan 45 ° \tan 20 ° \tan 40 ° \tan 50 ° \tan 70 °}{5}

(viii)

\frac{3 \cos 55 °}{7 \sin 35 °} - \frac{4 (\cos 70 ° cosec 20 °)}{7 (\tan 5 ° \tan 25 ° \tan 45 ° \tan 65 ° \tan 85 °)}

(ix)

\frac{\sin 18 °}{\cos 72 °} + \sqrt{3} \{\tan 10 ° \tan 30 ° \tan 40 ° \tan 50 ° \tan 80 °\}

(x)

\frac{\cos 58 °}{\sin 32 °} + \frac{\sin 22 °}{\cos 68 °} - \frac{\cos 38 ° cosec 52 °}{\tan 18 ° \tan 35 ° \tan 60 ° \tan 72 ° \tan 55 °}

Q. Prove that:

(i) \frac{\sin 70 °}{\cos 20 °} + \frac{cosec 20 °}{\sec 70 °} - 2 \cos 70 ° cosec 20 ° = 0 (ii) \frac{\cos 80 °}{\sin 10 °} + \cos 59 ° cosec 31 ° = 2 (iii) \frac{2 \sin 68 °}{\cos 22 °} - \frac{2 \cot 15 °}{5 \tan 75 °} - \frac{3 \tan 45 ° \tan 20 ° \tan 40 ° \tan 50 ° \tan 70 °}{5} = 1 (iv) \frac{\sin 18 °}{\cos 72 °} + \sqrt{3} (\tan 10 ° \tan 30 ° \tan 40 ° \tan 50 ° \tan 80 °) = 2 [CBSE 2008] (v) \frac{7 \cos 55 °}{3 \sin 35 °} - \frac{4 (\cos 70 ° cosec 20 °)}{3 (\tan 5 ° \tan 25 ° \tan 45 ° \tan 65 ° \tan 85 °)} = 1

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

Q. Evaluate :

\frac{cos 58^{\circ}}{sin 32^{\circ}} + \frac{sin 22^{\circ}}{cos 68^{\circ}} - \frac{cos 38^{\circ} csc 52^{\circ}}{tan 18^{\circ} tan 35^{\circ} tan 60^{\circ} tan 72^{\circ} tan 55^{\circ}}

\frac{3 \cos 55 °}{7 \sin 35 °} - \frac{4 (\cos 70 ° \cos e c 20 °)}{7 (\tan 5 ° \tan 25 ° \tan 45 ° \tan 65 ° \tan 85 °)}

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(i) 11324 (ii) 116 (iii) -2 (iv) 1 (v) 0 (vi) √3 (vii) 1 (viii) -17 (ix) 2 (x) 6−√33

(i) $\frac{113}{24}$

(ii) $\frac{11}{6}$

(iii) -2

(iv) 1

(v) 0

(vi) $\sqrt{3}$

(vii) 1

(viii) - $\frac{1}{7}$

(ix) 2

(x) $\frac{6 - \sqrt{3}}{3}$