Advertisements
Advertisements
Question
Prove the following identities:
`((sec θ - tan θ))/((sec θ + tan θ)) = (1 + 2 tan^2θ - 2 sec θ tan θ)`
Theorem
Advertisements
Solution
LHS = `((sec θ - tan θ))/((sec θ + tan θ)) xx ((sec θ - tan θ))/((sec θ - tan θ))`
= `(sec θ - tan θ)^2/((sec^2θ - tan^2θ)`
= (sec θ – tan θ)2
= sec2θ + tan2θ – 2 sec θ tan θ ...[∵ sec2θ = 1 + tan2θ]
= 1 + 2 tan2θ – 2 sec θ tan θ = RHS
shaalaa.com
Is there an error in this question or solution?
