wiz-icon
MyQuestionIcon
MyQuestionIcon
2
You visited us 2 times! Enjoying our articles? Unlock Full Access!
Question

Find the set of value of x satisfying the equality sin(xπ4)cos(xπ4)=1 and the inequality 2cos7xcos3+sin3>2cos2x

Open in App
Solution

sin(xπ4)cos(xπ4)=1
sinx212cosx[cosA2+sinA2]=1
2sinx2π/7=1
sinx=12x=45o
2cos7xcos3+sin3>2cos2xπ T(LCM of 2π7,π)
2π
sinx=±2x=π4,3π4
(1)π42cos7π/42(cos32+sin32)>2cosπ/2
1cos(3π/4)>1
1cos(3π/4)<0>1
x=π/4 is not solution
(2)3π42cos21π42cos(3π/4)>2cos3π/2
2(1/2)(ve)>1
1|cos(3π/4)|>1 x=3π4
x=2nπ+3π/4

1377920_1149803_ans_c6f3ea9761b54cc18b853c0a55ae5e09.png

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
General Solutions
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon