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