Class 10, Maths, Chapter 8, Exercise 8.3, Solutions
Q.1. Evaluate:
(i) $\frac{\sin \,\,{{18}^{0}}}{\cos \,\,{{72}^{0}}}$
(ii) $\frac{\tan \,\,{{26}^{0}}}{\cot \,\,{{64}^{0}}}$
(iii) cos 480 – sin 420
(iv) cosec 310 – sec 590
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Q.2. Show that:
(i) tan 48° tan 23° tan 42° tan 67° = 1
(ii) cos 38° cos 52° – sin 38° sin 52° = 0
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Q.3. If tan 2A = cot (A – 18°), where 2A is an acute angle, find the value of A.
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Q.4. If tan A = cot B, prove that A + B = 90°.
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Q.5. If sec 4A = cosec (A – 20°), where 4A is an acute angle, find the value of A.
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Q.6. If A, B and C are interior angles of a triangle ABC, then show that $\sin \left( \frac{B+C}{2} \right)=\cos \frac{A}{2}$
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Q.7. Express sin 67° + cos 75° in terms of trigonometric ratios of angles between 0° and 45°.
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Given, sin 67°+ cos 75°
=sin (90°-23°) + cos (90° – 15°)
(∵ sin (90°- θ) = cos θ)
= cos 23° + sin 15°