Tamilnadu State Board New Syllabus Samacheer Kalvi 9th Maths Guide Pdf Chapter 6 முக்கோணவியல் Ex 6.3 Textbook Questions and Answers, Notes.
TN Board 9th Maths Solutions Chapter 6 முக்கோணவியல் Ex 6.3
கேள்வி 1.
கீழ்க்காண்பனவற்றின் மதிப்பு காண்க.
i) \(\left(\frac{\cos 47^{0}}{\sin 43^{\circ}}\right)^{2}+\left(\frac{\sin 72^{\circ}}{\cos 18^{\circ}}\right)^{2}-2 \cos ^{2} 45^{\circ}\)
ii) \(\frac{\cos 70^{\circ}}{\sin 20^{\circ}}+\frac{\cos 59^{\circ}}{\sin 31^{\circ}}+\frac{\cos \theta}{\sin \left(90^{\circ}-\theta\right)}-8 \cos ^{2} 60^{\circ}\)
iii) tan 15° tan30° tan45° tan 60° tan 75°
விடை:
= 1 + 1 – 2 × \(\left(\frac{1}{\sqrt{2}}\right)^{2}\)
= 1 + 1 – 2 × \(\frac{1}{2}\)
= 1 + 1 – \(\frac{2}{2}\)
= 1 + 1 – 1
= 0
ii) \(\frac{\cos 70^{\circ}}{\sin 20^{\circ}}+\frac{\cos 59^{\circ}}{\sin 31^{\circ}}+\frac{\cos \theta}{\sin \left(90^{\circ}-\theta\right)}-8 \cos ^{2} 60^{\circ}\)
= \(\frac{\cos \left(90^{\circ}-20^{\circ}\right)}{\sin 20^{\circ}}+\frac{\cos \left(90^{\circ}-31^{\circ}\right)}{\sin 31^{\circ}}+\frac{\cos \theta}{\cos \theta}-\) \(8 \times\left(\frac{1}{2}\right)^{2}\)
= \(\frac{\sin 20^{\circ}}{\sin 20^{\circ}}+\frac{\sin 31^{\circ}}{\sin 31^{\circ}}+\frac{\cos \theta}{\cos \theta}-8 \times\left(\frac{1}{4}\right)\)
= 1 + 1 + 1 – 2
= 3 – 2
= 1
iii) tan 15° tan30° tan45° tan 60° tan 75°
= tan (90° – 75°) tan30° tan 45o tan 60° tan 75°
= cot 75° × \(\frac{1}{\sqrt{3}}\) × 1 × \(\sqrt{3}\) × tan 75°
= \(\frac{1}{\tan 75^{\circ}} \times \frac{1}{\sqrt{3}} \times 1 \times \sqrt{3} \times \tan 78^{\circ}\)
= 1
