Question

sinA/(1+cosA)+(1+cosA)/sinA=2cosecA. prove that.​

Answer 1

Step-by-step explanation:

question: sinA/(1+cosA)+(1+CosA)/SinA

solution: sin^2A+(1+CosA)^2/(1+cosA)SinA

= sin^2A+1^2+cos^2+2CosA/(1+cosA)sinA

=1+1+2cosA/(1+cosA)sinA (Note :(sin^2A+Cos^2A)=1

=(2+2cosA)/(1+CosA)sinA

=2(1+CosA)/(1+cosA)sinA

=2*1/sinA

Note : sin theta= 1/ cosec Theta

= 2* 1/1/cosecA

= 2 cosec A

prooved