Advertisements
Advertisements
Question
सिद्ध कीजिए: `2 cos pi/13 cos (9pi)/13 + cos (3pi)/13 + cos (5pi)/13 = 0`
Sum
Advertisements
Solution
बायाँ पक्ष = `2 cos pi/13 cos (9pi)/13 + cos (3pi)/13 + cos (5pi)/13`
= `cos (pi/13 + (9pi)/13) + cos (pi/13 - (9pi)/13) + cos (3pi)/13 + cos (5pi)/13`
= `cos (10pi)/13 + cos (8pi)/13 + cos (3pi)/13 + cos (5pi)/13` [2cos x cos y = cos(x + y) + cos (x - y)]
= `cos (pi - (13pi)/13) + cos (pi - (8pi)/13) + cos (3pi)/13 + cos (5x)/13`
= `- cos (3pi)/13 - cos (5pi)/13 + cos (3pi)/13 + cos (5pi)/13` [∵ cos (π - θ) = -cosθ]
= 0 = दायाँ पक्ष।
shaalaa.com
त्रिकोणमितीय फलन - त्रिकोणमितीय फलनों का प्रांत तथा परिसर
Is there an error in this question or solution?
