Let x = 4sin^2 10^o +4sin^2 50^o cos20^o +cos80^o and y = cos^2 (π/5)+cos^2 ((2π)/(15))+cos^2 ((8π)/(15)). find x+y ?


Question and Answers Forum

All Questions Topic List
Trigonometry Questions
Previous in All Question Next in All Question
Previous in Trigonometry Next in Trigonometry
Question Number 29581 by math solver last updated on 10/Feb/18

$L e t x = 4 {s i n}^{2} 10^{o} + 4 {s i n}^{2} 50^{o} c o s 20^{o} + c o s 80^{o}$ $a n d y = {c o s}^{2} \frac{π}{5} + {c o s}^{2} \frac{2 π}{15} + {c o s}^{2} \frac{8 π}{15} .$ $f i n d x + y ?$
	Answered by ajfour last updated on 10/Feb/18

	$x = 2 + \frac{1}{2}; y = 1 + \frac{1}{2}; x + y = 4$ $x = 2 (1 - \cos 20 °) + 2 (1 + \cos 80 °) \cos 20 °$ $+ \cos 80 °$ $x = 2 + \cos 80 ° + 2 \cos 80 ° \cos 20 °$ $= 2 + \cos 80 ° + \cos 100 ° + \cos 60 °$ $= 2 + \cos 80 ° - \sin 10 ° + \frac{1}{2}$ $\Rightarrow x = 2 + \frac{1}{2}$ $. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .$ $y = \frac{1}{2} [1 + \cos \frac{2 π}{5} + 1 + \cos \frac{4 π}{15} + 1 + \cos \frac{16 π}{15}]$ $= \frac{3}{2} + \frac{1}{2} [\cos \frac{6 π}{15} + \cos \frac{4 π}{15} - \cos \frac{π}{15}]$ $= \frac{3}{2} + \frac{1}{2} [2 \cos \frac{π}{3} \cos \frac{π}{15} - \cos \frac{π}{15}]$ $\Rightarrow y = \frac{3}{2} + 0$ $\Rightarrow x + y = 4 .$
	Commented by math solver last updated on 11/Feb/18

	$thank you sir .$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum