CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

If (sec A – tan A) = x then prove that 1+x21-x2= cosec A.

Open in App
Solution


Given: secA-tanA=x .....1
We know
sec2A-tan2A=1secA+tanAsecA-tanA=1 a2-b2=a-ba+bsecA+tanAx=1 From 1secA+tanA=1x .....2
Adding (1) and (2), we get
secA-tanA+secA+tanA=x+1x2secA=x2+1xsecA=x2+12x .....3
Subtracting (1) from (2), we get
secA+tanA-secA+tanA=1x-x2tanA=1-x2xtanA=1-x22x .....4
Dividing (3) by (4), we get
1+x22x1-x22x=secAtanA1+x21-x2=1cosAsinAcosA1+x21-x2=1sinA1+x21-x2=cosecA

flag
Suggest Corrections
thumbs-up
23
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Differentiating One Function wrt Other
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon