Question
Question: If \(\alpha = 22{^\circ}30',\) then \((1 + \cos\alpha)(1 + \cos 3\alpha)\) \((1 + \cos 5\alpha)(1 + ...
If α=22∘30′, then (1+cosα)(1+cos3α) (1+cos5α)(1+cos7α) equals
A
1/8
B
1/4
C
221+2
D
2+12−1
Answer
1/8
Explanation
Solution
We know, sin2221o=212−2and
cos2221o=212+2
∴(1+cos2221o)(1+cos6721o)(1+cos11221o)
(1+cos15721o)
=(1+212+2)(1+212−2)(1−212−2)
(1−212+2)
=[1−41(2+2)][1−41(2−2)] =16(4−2−2)(4−2+2)
=16(2−2)(2+2)=164−2=81.