if a and b are complementary angles then what is the value of cosecB*secA-cotB*tanA
Answers & Comments
bharatdetha
What i prefer is in sin and cos form so i will first convert cosecB*secA in sin and cos 1/(sinB*cosA) = 1/(sin(90-A)*cosA) =1/cos^2A now cotB*tanA = (cosB*sinA)/(sinB*cosA) =(cos(90-A)*sinA)/cos^2A =sin^2A/cos^2A now the total term together cosecB*secA- cotB*tanA =1/cos^2A - sin^2A/cos^2A = (1-sin^2A)/cos^2A =cos^2A/cos^2A =1
Answers & Comments
i will first convert cosecB*secA in sin and cos
1/(sinB*cosA)
= 1/(sin(90-A)*cosA)
=1/cos^2A
now
cotB*tanA
= (cosB*sinA)/(sinB*cosA)
=(cos(90-A)*sinA)/cos^2A
=sin^2A/cos^2A
now the total term together
cosecB*secA- cotB*tanA
=1/cos^2A - sin^2A/cos^2A
= (1-sin^2A)/cos^2A
=cos^2A/cos^2A
=1