wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Let f(x)=1sin2x+cos2x2cos2x and α+β=5π4. Then the value of f(α)f(β) is

A
1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
12
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B 12
f(x)=1sin2x+cos2x2cos2x
f(x)=2cos2x2sinxcosx2(cos2xsin2x)
f(x)=cosxcosx+sinx=11+tanx

Now, f(α)f(β)=(11+tanα)⎜ ⎜ ⎜ ⎜11+tan(5π4α)⎟ ⎟ ⎟ ⎟
=(11+tanα)⎜ ⎜ ⎜11+1tanα1+tanα⎟ ⎟ ⎟
=(11+tanα)(1+tanα2)
=12

flag
Suggest Corrections
thumbs-up
1
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Multiple and Sub Multiple Angles
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon