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

If cos4θ+cos2θ=1 then show that
i) sec4θsec2θ=1
ii) cot4θcot2θ=1

Open in App
Solution

Given: cos4θ+cos2θ=1
cos4θ=1cos2θ
cos4θ=sin2θ(1)
Now,
(1)sec4θsec2θ
=1cos4θ1cos2θ
=1cos2θcos4θ
=sin2θcos4θ
=sin2θsin2θ(from(1))
=1
(2)cot4θcot2θ
=cos4θsin4θcos2θsin2θ
=cos4θsin2θcos2θsin4θ
=sin2θsin2θcos2θsin4θ[from(1)]
=sin2θ(1cos2θ)sin4θ
=sin2θ×sin2θsin4θ
=sin4θsin4θ
=1

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