Prove that: (1+cotA−cosecA)(1+tanA+secA)=2<p></p>

LHS =1+cotA−cosecA=1+cosA/sinA−1/sinA=(sinA+cosA−1)/sinA
1+tanA+secA=1+sinA/cosA+1/cosA=(cosA+sinA+1)/cosA
(1+cotA−cosecA)(1+tanA+secA)=(sinA+cosA−1)(sinA+cosA+1)/(sinAcosA)
=(sinA+cosA)²−1²/sinAcosA
=(sin²A+cos²A+2sinAcosA−1)/sinAcosA
=(1+2sinAcosA−1)/sinAcosA
=2sinAcosA/sinAcosA
=2=RHS
Hence Proved

Eduprobe

Question:

Prove that: (1+cotA−cosecA)(1+tanA+secA)=2

Solution: