CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
Question

Evaluate the following : (1+tanA+secA)(1+cotA-cosecA).


Open in App
Solution

Evaluate (1+tanA+secA)(1+cotA-cosecA).

Convert the given expression into sineandcosine

(1+tanA+secA)(1+cotA-cosecA)=1+sinAcosA+1cosA1+cosAsinA-1sinAtanA=sinAcosA,secA=1cosA,cotA=cosAsinA,cosecA=1sinA=cosA+sinA+1cosAsinA+cosA-1sinA=(sinA+cosA)2-1sinA·cosA(a+b)(a-b)=a2-b2=sin2A+cos2A+2sinA·cosA-1sinA·cosA(a+b)2=a2+b2+2ab=1+2sinA·cosA-1sinA·cosA=2sinA·cosAsinA·cosA=2

Hence, the required answer is (1+tanA+secA)(1+cotA-cosecA)=2.


flag
Suggest Corrections
thumbs-up
2
BNAT
mid-banner-image